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CENTRE OF MASS, COLLISSION AND LINEAR MOMENTUM 1. A particle A suffers an oblique elastic collision with a particle B that is at rest initially. If their masses are the same, then, after the collision : a) they will move in original direction while B remains at rest b) A continues to move in the original direction while B remains at rest c) they will move in mutually perpendicular directions. d) A comes to rest and B starts moving in the direction of the original motion of A. 2. A metal ball hits a wall and does not rebound whereas a rubber ball of the same mass of hitting the wall with the same velocity rebounds back. It can be concluded that : a) metal ball suffers greater change in momentum b) rubber ball suffers greater change in momentum c) the initial momentum of metal ball is greater than initial momentum of rubber ball d) both suffer same change in momentum. 3. A ball hits the floor and rebounds after inelastic collision. In this case a) the momentum of the ball just after the collision is the same as that just before the collision b) the mechanical energy of the ball remains the same in the collision c) the total momentum of the ball and the earth is conserved d) the total mechanical energy of the ball and the earth is conserved. 4. A shell initially at rest explodes in two equal fragments A and B. Then a) A and B have collinear velocities in the same direction b) A and B have equal speeds but opposite velocities c) A and B have equal speeds but their velocities inclined to each other d) A and B may have unequal speeds but opposite velocities. 5. A space craft of mass M is moving with velocity v in free space when it explodes and breaks in two. After the explosion, a mass m of the space craft is left stationery. What is the velocity of other part ? a) Mv / ( M - m ) b) Mv / ( M + m ) c) Mv / ( m - M ) d) ( M + m ) v/M 6. A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is a) c a b b + . b) a a c b + . c) a b c a + . d) a c a b + . 7. A bullet of mass m moving with velocity v strikes a suspended wooden block of mass M at rest. If the collision is inelastic block rises to a height h, the initial velocity of the bullet will be a) ( ) 2 gh b) ( ) ( ) M m m gh + 2 c) m M m gh ( ) ( ) + 2 d) ( ) ( ) M m M gh + 2 8. A ball is dropped from a height h on the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds is a) 2 he b) he c) h e 2 d) 2 e h 9. A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass. If e is the coefficient of restitution, then ratio of velocities of the two spheres after collision will be a) 1 1 + e e b) 1 1 + e e c) e e + 1 1 d) e e + 1 1 10. A radioactive nucleus initially at rest decays by emitting an electron and neutron at right angles to one another. The momentum of the electron is 3.2 × 10 -23 kg-m/sec and that of the neutron is 6.4 × 10 -23 kg-m/sec. The direction of the recoiling nucleus with that of the electron motion is a) tan -1 ( 0.5 ) b) tan -1 ( 2 ) c) π - tan -1 ( 2 ) d) π / 2 + tan -1 (2) www.IITwikipedia.com

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CENTRE OF MASS, COLLISSION AND LINEAR MOMENTUM

1. A particle A suffers an oblique elastic collision with a particle B that is at rest initially. If their masses are the same, then, after the collision :a) they will move in original direction while B remains at restb) A continues to move in the original direction while B remains at restc) they will move in mutually perpendicular directions.d) A comes to rest and B starts moving in the direction of the original motion of A.

2. A metal ball hits a wall and does not rebound whereas a rubber ball of the same mass of hitting the wall with the same velocity reboundsback. It can be concluded that :a) metal ball suffers greater change in momentumb) rubber ball suffers greater change in momentumc) the initial momentum of metal ball is greater than initial momentum of rubber balld) both suffer same change in momentum.

3. A ball hits the floor and rebounds after inelastic collision. In this casea) the momentum of the ball just after the collision is the same as that just before the collisionb) the mechanical energy of the ball remains the same in the collisionc) the total momentum of the ball and the earth is conservedd) the total mechanical energy of the ball and the earth is conserved.

4. A shell initially at rest explodes in two equal fragments A and B. Thena) A and B have collinear velocities in the same directionb) A and B have equal speeds but opposite velocitiesc) A and B have equal speeds but their velocities inclined to each otherd) A and B may have unequal speeds but opposite velocities.

5. A space craft of mass M is moving with velocity v in free space when it explodes and breaks in two. After the explosion, a mass m of thespace craft is left stationery. What is the velocity of other part ?a) Mv / ( M - m ) b) Mv / ( M + m ) c) Mv / ( m - M ) d) ( M + m ) v/M

6. A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is

a)ca b

b+. b)

aa c

b+. c)

a bc

a+ . d)a ca

b+ .

7. A bullet of mass m moving with velocity v strikes a suspended wooden block of mass M at rest. If the collision is inelastic block rises to aheight h, the initial velocity of the bullet will be

a) ( )2gh b)( ) ( )M mm

gh+ 2 c)m

M mgh

( )( )

+2 d)

( ) ( )M mM

gh+ 2

8. A ball is dropped from a height h on the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds is

a) 2he b) he c)he2

d) 2eh

9. A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass. If e is the coefficient of restitution,then ratio of velocities of the two spheres after collision will be

a)11−+ee b)

11+−ee c)

ee+−11

d)ee−+11

10. A radioactive nucleus initially at rest decays by emitting an electron and neutron at right angles to one another. The momentum of theelectron is 3.2 × 10-23 kg-m/sec and that of the neutron is 6.4 × 10-23 kg-m/sec. The direction of the recoiling nucleus with that of the electronmotion isa) tan-1 ( 0.5 ) b) tan-1 ( 2 ) c) π - tan-1 ( 2 ) d) π / 2 + tan-1 (2)

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11. A shell is fired from a canon with velocity v m/sec at an angle q with the horizontal direction. At the highest point in its path, it explodes into two piecesof equal mass. One of the pieces retraces its path to the canon and the speed in m/sec of the other piece immediately after the explosion is

a) 3 v cos θ b) 2 v cos θ c) 3/2 . v cos θ d) 3 2/ . v cos θ

12. Two solid rubber balls, A and B having masses 200 and 400 gm respectively are moving in opposite directions with velocity of A equal to0.3 m/sec. After collision, the two balls come to rest when the velocity of B isa) 0.15 m/sec b) 1.5 m/sec c) 0.3 m/sec d) none of these

13. A ball is allowed to fall from a height of 10 m. If there is 40% loss of energy due to impact, then after one impact ball will go up to

a) 10 m b) 8 m c) 4 m d) 6 m

14. A bag P ( mass M ) hangs by a long thread and a bullet ( mass m ) comes horizontally with velocity v and gets caught in the bag. Then forthe combined ( bag + bullet ) system

a) momentum is mvMM m+ b) kinetic energy is

mv2

2

c) momentum is mv M m

M( )+

d) kinetic energy is m vM m

2 2

2 ( )+15. A bullet is fired from a gun, which is free to recoil. Then the K.E. of the recoil of the gun is

a) greater than that of the bullet b) equal to that of the bulletc) less than that of the bulletd) equal to loss in potential energy of the spring system in the gun.

16. A body of mass M at rest explodes into three pieces, two of which of mass M/4 each, are thrown off inperpendicular directions with velocities of 3 m/s and 4 m/s respectively. The third piece will be thrownoff with a velocity of :

a) 1.5 m/s b) 2.0 m/sc) 2.5 m/s d) 3.0 m/s

17. A and B are two identical masses, at rest, suspended by an inextensible string passing over a smoothfrictionless pulley. Particle A is given a push downwards with a speed u. It collides elastically with the floor and rebounds. Immediately aftercollision,a) both A and B are at rest. b) A moves upwards and B downwards with equal speed.c) A and B both move upwards with unequal speed. (d) A and B both move upwards with equal speed.

18. A pendulum consists of a wooden bob of mass m and length l. A bullet of mass m1 is fired towards the pendulum with a speed v1. The bulletemerges out of the bob with a speed v1/3, and the bob just completes motion along a vertical circle. Then v1 is

a)mm

gl1

5FHGIKJ b)

32 1

mm

glFHGIKJ (5 ) c)

23

1mm

glFHGIKJ (5 ) d)

mm

gl1FHGIKJ ( )

19. A block of mass 1 kg moving with speed 4 m/s collides with another block of mass 2 kg at rest. The lighter block comes to rest after collision.The loss of K.E. of the system isa) 8 joule b) 4 × 10-7 joule c) 4 joule d) none of these

20. On a stationery sail-boat, air is blown at the sails from a fan attached to the boat. The boat willa) remain stationary b) spin around c) move in a direction opposite to that in which air is blownd) move in the direction in which the air is blown.

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21. The engines of a jet aircraft apply a thrust force of 105 N during take off and cause the plane to attain a velocity of 1 km/sec in 10 seconds. Themass of the plane is

a) 102 kg b) 103 kg c) 104 kg d) 105 kg

22. Two particles A and B, initially at rest, move towards each other under a mutual force of attraction. At the instant, when the speed of A is Vand the speed of B is 2V, the speed of the cm of the system isa) zero b) V c) 1.5 V d) 3 V

23. A block of mass m rests on a wedge of mass M, which, in turn, rests on a horizontal table (see figure ). All surfaces are frictionless. If theblock starts from rest,

a) the position of the cm of the system will change along both horizontal and vertical directions.b) the position of the cm of the system will change along the vertical but not along the horizontal

directionc) the position of the cm of the system will change along the horizontal but not along the vertical

directiond) nothing can be said about the position of the cm

24. Two particles P and Q are initially at rest and 1 m apart. P has a mass of 1 kg and Q a mass of 3 kg. Due to mutual attraction, P and Q movetowards each other. They collide at a distancea) 0.25 m from P b) 0.25 m from Q c) 0.5 m from Q d) 0.5 m from P

25. Two particles P and Q of mass 1 kg and 3 kg, respectively, move towards each other under mutual attraction with velocities 30 m s-1 and6 m s-1. The velocity of their cm isa) 36 m s-1 b) 18 m s-1 c) 3 m s-1 d) none of these

26. If two particles of masses m1 and m2 move with speeds v1 and v2 towards each other on a smooth horizontal table, the speed of their cmis

a)m v m vm m1 1 2 2

1 2

++ b)

m v m vm m1 1 2 2

1 2

−+ c)

m v m vm m1 2 2 1

1 2

++ d)

m v m vm m1 2 2 1

1 2

−+

27. The position coordinates ( x, y ) of the CG of the L-shaped plate with reference to the origin at the lower left-hand corner are

a) x = 11 cm, y = 9 cm b) x = 7 cm, y = 9 cm

c) x = 3 cm, y = 10 cm d) x = 14 cm, y = 8 cm

28. The position coordinates ( , )x y of the cm of the T-shaped plate with reference to the frameshown in the figure are

a) x = 0, y = 8 cm b) y = 203

, x = 203

cm

c) y = 0, x = 203

cm d) x = 0, y = 203

cm

29. Two masses m1 and m2 are separated by a distance l. The distance of their cm from m1 is

a)m lm m

1

2+ b)m lm m

2

1 2+ c)mml1

2d)mml2

1

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30. A body of a mass 1m is moving with a velocity v. It collides with another stationary body of mass 2m . They get embedded. At the point of collision,the velocity of the systema) increases b) decreases c) remains samd) becomes zero

Answers

1. c 2. b 3. c 4. b 5. a 6. b7. b 8. a 9. a 10. c 11. a 12. a13. d 14. d 15. c 16. c 17. d 18. b19. c 20. a 21. b 22. a 23. b 24. b25. c 26. b 27. d 28. a 29. b 30. c

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FLUIDS STATICS AND DYNAMICS

1. A boat full of scrap iron is floating on water in a lake. If all the iron is dropped into water, will the level of watera) go up b) remain the same c) rise very high d) go down

2. In order that a floating object be in a stable equilibrium, its centre of buoyancy should bea) vertically above its centre of gravity b) vertically below its centre of gravityc) horizontally in line with its centre of gravity d) may be anywhere.

3. A piece of ice is floating in a jar containing water. When the ice metls, then the level of watera) rises b) fallsc) remains unchanged d) rises or falls depending upon the mass ice.

4. A piece of ice having a stone frozen in it floats in a glass vessel filled with water. How will the level of water in the vessel change when theice meltsa) the level will rise b) the level will not change c) the level will drop d) some water will flow out

5. A body floats in a liquid contained in a beaker. The whole system is falling under gravity. The upthrust on the body due to liquid isa) zero, b) equal to weight of liquid displaced,c) equal to weight of the body in air, d) equal to the weight of the immersed body.

6. A balloon filled with air is weighted, so that it barely floats in water as shown in figure. When it is pushed down so thatit gets submerged a short distance in water, then the balloon

a) will come up again to its former position b) will remain in the position it is leftc) will sink to the bottom d) will emerge out of liquid.

7. A jet plane flies in air becausea) the thrust of the jet compensates for the force of gravityb) the weight of the air whose volume is equal to the volume of the plane is more than the weight of planec) the flow of air around the wings causes an upward force which compensates for the force of gravityd) the gravity does not act on bodies moving with speed.

8. In the figure shown, the flow of liquid is through a horizontal pipe. Three tubes A, B and C are connected to the pipe. The radii of the tubes

A, B and C at the junction are respectively 2 cm, 1 cm and 2 cm. It can be said that the

AB

C

a) height of the liquid in the tube A is maximum. b) height of the liquid in the tubes A and B is the samec) height of the liquid in all the three tubes is the same d) height of the liquidin the tubes A and C is the same.

9. A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one of thewalls at a depth h below the surface of water (see figure). Express the horizontal distance x interms of H and h

a) x h H h= −( ) b) x h H h= −[ ( ) / ]2

c) x h H h= −2 ( ) d) x h H h= −4 ( )

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10. As shown in the figure, water squirts horizontally out of two holes in the side of the cylinder and thetwo streams strike the ground at the same point. If the hole Q is at a height h above the ground andthe level of water stands at height H above the ground, then the height of P above ground level is

a) 2 h b) H / hc) H - h d) H / 2

11. A liquid flows in the tube from left to right as shown in figure. A1 and A2 are the cross-sections of the portions of the tube as shown. Thenthe ratio of speeds v1 / v2 will be

V1

1A 2A2V

a) A A1 2/ b) A A2 1/ c) A A2 1/ d) A A1 2/

12. When a large bubble rises from the bottom of a lake to the surface, its radius doubles. The atmospheric pressure is equal to that of acolumn of water of height H. The depth of the lake isa) H b) 2H c) 7H d) 8H

13. Two vessels A and B have the same base area and contain water to the same height, but the mass of water in A is two times that in B. The ratio

of the liquid thrust at the base of A to that at the base of B is

a) 4 : 1 b) 2 : 1c) 1 : 1 d) 16 : 1

14. The spring balance A reads 2 kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan ofthe balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in figure. In thissituation

a) the balance A will read more than 2 kg,b) the balance B will read less than 5 kg,c) the balance A will read less than 2 kg and B will read more than 5 kg,d) the balance A and will B will read 2 kg and 5 kg respectively.

15. A wooden cube just floats inside water when a 200 gm mass is placed on it. When the mass is removed, the cubeis 2 cm above the water level. The size of the cube isa) 5 cm b) 10 cm c) 15 cm d) 20 cm

16. The volume of an air bubble is doubled as it rises from the bottom of a lake to its surface. The depth of the lake isa) 5 m b) 10 m c) 30 m d) 50 m.

17. A vessel contains oil (density = 0.8 gm/cm2 ) over mercury (density = 13.6 gm/cm2 ). A homogeneous sphere floats with half of its volumeimmersed in mercury and the other half in oil. The density of material of the sphere in gm/cm3 is

a) 3.3 b) 6.4 c) 7.2 d) 2.8

18. A body floats with one-third of its volume outside water and 1/4 of its volume outside another liquid. The density of other liquid isa) 9/4 gm/cc b) 4/9 gm/cc c) 8/9 gm/cc d) 2/9 gm/cc

A

m

B

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19. The diagram shows a venturimeter, through which water is flowing. The speed of water at X is 2 cm/s. The speed of water atY ( taking g = 1000 cms–2 ) is

XY

5.1 mm

a) 23 cm-1 b) 32 cm-1 c) 101 cm-1 d) 1024 cm-1

20. The fraction of a floating object of volume V0 and density d0 above the surface of a liquid of density d will be

a)dd

0 b)ddd d

0

0+ c)d dd− 0 d)

dd d

0

0−

21. A cylinder is filled with a liquid of density d upto a height h. If the beaker is at rest, then the mean pressure on the wall is

a) zero b) h d g c)h d g2 d) 2 h d g

22. If in above question, the cylinder is placed in a lift which is moving upwards with an acceleration a, then the pressure on the bottom is

a) h d g b)12hd g c) h d ( g + a ) d) h d ( g - a )

23. A plate of area 0.5 m² and thickness 40 mm is immersed in water vertically. The thrust on the plate due to water ( g = 10 m s-2 ) isa) 1000 N m-2 b) 500 N m-2 c) 200 N m-2 d) 1250 N m-2

24. Equal volumes of two substances are mixed. Their densities are 1ρ and 2ρ The density of their mixture, assuming no contraction is

a)21

21ρρρρ +

b) ρ ρ1 2

2+ c) ρ ρ1 2 d) ρ ρ

ρ ρ1 2

1 2+25. Equal weights of two liquids are mixed. Their densities are 1ρ and 2ρ . The density of their mixture, assuming no contraction is

a)ρ ρ1 2

1 2

+P P

b) ρ ρ1 2

2+ c) ρ ρ1 2 d)

21

212ρρρρ

+

26. A beaker containing water is placed on the platform of a spring balance. The balance reads 1.5 kg. A stone of mass 1/2 kg and volume0.001 m3 is immersed in water without touching the wall of the beaker. The balance readsa) 2 kg b) 1.5 kg c) 1.0 kg d) 2.5 kg

27. The gate of a canal is 5 m wide, and the water levels on either side of it are 20 m and 12 m. The resultant thrust on the gate (g = 10ms–2)isa) 64 × 105 N b) 64 × 103 N c) 64 × 104 N d) 64 × 107 N

28. Mercury is poured into communicating vessels of different cross sections. An iron piece is dropped into the broad vessel. The level ofmercurya) will go down by unequal amounts, b) will go down by equal amounts,

c) will go up by unequal amounts, d) will go up by equal amounts.

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29. A body of mass m, lighter than water floats in water ( density = oρ ) in a cylinder of large area S. The change in the level of water in the vesselis

a) S/m oρ b) m/Soρ c) ρ0 /m d) m / ρ0

30. A ball whose density is ρ falls into water of density °ρ from a height h above the water surface. If °< ρρ , the depth to which the ball

will sink is

a) hρ ρ0 / b) ρ ρ ρh / ( )0 − c) ρ ρ ρ0 0h / ( )− d) hρ ρ/

Answers

1. d 2. a 3. c 4. c 5. a 6. c7. c 8. d 9. c 10. c 11. b 12. c13. c 14. c 15. b 16. b 17. c 18. c19. b 20. c 21. c 22. c 23. c 24. b25. d 26. d 27. a 28. d 29. a 30. b

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GEOMETRICAL OPTICS

1. When a ray light enters a glass slab from aira) its wavelength decreases b) its wavelength increasesc) its frequency increases d) neither wavelength nor frequency changes

2. When a point object is seen by an observer through a glass slab, the image isa) seen nearer to the observer, but beyond the slab b) at the same distance from the observer as the object isc) seen farther from the observer d) seen near to the observer but between the slab and the observer

3. If ijµ represents the refractive index when a light ray goes from medium 'i' to medium 'j' then the product µ µ µ21 32 43× × is equal to

a) µ32 b) µ42 c) µ31 d) 1/µ14

4. A well cut diamond appears bright becausea) it emits light b) it is radioactive c) of total internal reflection d) it has high density

5. One can not see through fog becausea) fog absorbs light b) light is scattered by the droplets in a fogc) light suffers total reflection at the droplet in a fog d) the refractive index of fog is infinity

6. A driver in a swimming pool wants to signal his distress to a person lying on the edge of the pool by flashing his water proof flash lighta) he must direct the beam vertically upwardsb) he has to direct the beam horizontallyc) he has to direct the beam at an angle to the vertical which is slightly less than the critical angle of incidence for total internal reflectiond) he has to direct the beam at an angle to the vertical which is slightly more than the critical angle of incidence for total internal reflection

7. A ray of light travelling inside a rectangular glass block of refractive index 2 is incident on the glass-air surface at an angle of incidenceslightly less than 45°. The refractive index of air is one. Under these conditions the raya) will emerge into the air without any deviation b) will be reflected back into the glassc) will be absorbed d) will emerge into the air with an angle of refraction equal to 90°.

8. The critical angle for light going from medium X into medium Y is θ . The speed of light in medium X is v. The speed of light in medium Yis

a) v ( cos )1− θ b) v / sinθ c) v / cosθ d) v cosθ9. Monochromatic light of wavelength 1λ travelling in a medium of refractive index n1 enters a denser medium of refractive index n2. The

wavelength in the second medium is

a) 1λ ( n1 / n2 ) b) 1λ ( n2 / n1 ) c) 1λ ( n1 - n2 ) / n2 d) 1λ ( n2 - n1 ) / n1

10. A beam of light is converging towards a point I on a screen. A plane parallel plate of glass whose thickness is in the direction of beam = t,refractive index = µ is introduced in the path of the beam. The convergence point is shifted by

a) t 1 1−FHGIKJµ away b) t 1 1

+FHGIKJµ away c) t 1 1

−FHGIKJµ nearer d) t 1 1

+FHGIKJµ nearer

11. A ray of light from a denser medium strikes a rare medium at angle of incidence i (see figure). The reflected and refracted rays make anangle of 90° with each other. The angles of reflection and refraction are r and r'. The critical angle is

a) )r(cotsin 1− b) sin (tan )−1 i c) sin (tan ' )−1 r d) tan (sin )−1 i

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12. Keeping the incident ray fixed, if a plane mirror is rotated through an angle θ about an axis lying in its plane, then the reflected ray turns throughangle

a) 0 b) 2θ c) θ / 2 d) 4θ

13. A plane glass slab is placed over various coloured letters. The letter which appears to be raised the least is

a) violet b) yellow c) red d) green

14. A vessel of depth 2d cm is half filled with a liquid of refractive index 1µ and the upper half with a liquid of refractive index 2µ . The apparent depthof the vessel seen perpendicularly is

a)µ µµ µ

1 2

1 2+FHG

IKJ d b)

1 1

1 2µ µ+

FHG

IKJ d c)

1 1 21 2µ µ+

FHG

IKJ d d)

1 21 2µ µFHGIKJ d

15. A lens forms a sharp image on a screen. On inserting a parallel-sided slab of glass between the lens and the screen it is found necessaryto move the screen a distance d away from the lens in order for the image to be again sharply focused. If the refractive index of glassrelative to air is µ , then the thickness of the slab is

a)dµ

b)µd

c)µµd

( )−1d)

( )µµ−1 d

16. A bird in air looks at a fish vertically below it and inside water. h1 is the height of the bird above the surface of water and h2, the depth of thefish below the surface of water. If refractive index of water with respect to air be µ , then the distance of the fish as observed by the bird is

a) h h1 2+ b) h h1

2+µ

c) µh h1 2+ d) µ µh h1 2+

17. A fish is a little away below the surface of a lake. If the critical angle is 49°, then the fish could see things above the water surface within anangular ring of °θ where

a) θ = 49° b) θ = 90°

c) θ = 98° d) θ = 24½°

18. A short linear object of length L lies on the axis of a spherical mirror of focal length f at a distance ufrom the mirror. Its image has an axial length 'L' equal to

a) Lf

u f−LNMOQP

1 2/

b) Lu ff

( )/

+LNM

OQP

1 2

c) Lu ff

( )−LNM

OQP

2

d) Lf

u f( )−LNM

OQP

2

19. A concave mirror of focal length f produces an image n times the size of the object. If the image is real then the distance of the object fromthe mirror is,

a) ( )n f−1 b) {( ) / }n n f−1 c) {( ) / }n n f+1 d) ( )n f+1

20. In a concave mirror an object is placed at a distance x1 from the focus and the image is formed at a distance x2 from the focus. Then thefocal length of the mirror is

a) x x1 2 b) x x1 2 c) ( ) /x x1 2 2+ d) x x1 2/

21. A converging lens is used to form an image on a screen. When the upper half of the lens is covered by an opaque screena) half the image will disappear b) complete image will disappearc) intensity of image will increase d) intensity of the image will decrease

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22. A double convex lens made of material of refractive index 1.5 and having a focal length of 10 cm is immersed in a liquid of refractive index 3.0.The lens will behave asa) converging lens of focal length 10 cm b) diverging lens of focal length 10 cmc) converging lens of focal length 10/3 cm d) converging lens of focal length 30 cm

23. Two lenses of power + 12 and -2 diopters are placed in contact. What will be the focal length of the combinationa) 10 cm b) 12.5 cm c) 16.6 cm d) 8.33 cm

24. f B and f R are the focal lengths of a convex lens for blue and red light respectively and BF and RF are the focal lengths of a concave lensfor blue and red light respectively. We must then havea) f f F FB R B R< <and b) f f F FB R B R< >and c) f f F FB R B R> >and d) f f F FB R B R> <and

25. When a pencil of white light which is parallel to principal axis, is refracted by a converging lens, then the rays converge on the principal axis,the focus point being spread out over a short range along the principal axis. If a screen is put perpendicular to the principal axis, at thefarthest focus point, the image on the screen isa) a sharp white or violet point b) a sharp red pointc) a circular dispersed patch, red at the centre and violet at the border d) a circular dispersed patch, violet at thecentre and red at the border.

26. A real image is formed by a convex lens. A concave lens is now placed adjacent to the convex lens, again the real image is formed. Thiswilla) shift towards the lens system b) shift away from the lens systemc) remain in its original position d) shift to infinity

27. A concave mirror and a convex lens are of the same focal length in air. When they are immersed in watera) the concave mirror will have its focal length increased b) the convex lens will have its focal length increased.c) they will have equal focal lengths, different from those in air d) they will have equal focal lengths, same as those in the air.

28. A thin lens has focal length f, and its aperture has diameter d. It forms an image of intensity I. Now, the central part of the aperture uptodiameter d / 2 is blocked by an opaque paper. The focal length and image intensity will change toa) f /2 and I/2 b) f and I/4 c) 3f /4 and I/2 d) f and 3I/4

29. The least distance between a point object and its real image formed by a convex lens of focal length F isa) 2F b) 3 F c) 4 F d) greater than 4 F

30. A convex lens of focal length A and a concave lens of focal length B are placed in contact. The focal length of the combination is

a) ( A + B ) b) ( A - B ) c)ABA B( )+ d)

ABB A( )−

31. A convex lens of focal length f is placed some where in between an object and a screen. The distance between the object and the screenis x. If the numerical value of the magnification produced by the lens is m, the focal length of the lens is

a) ( )21+mmx

b)mxm( )−1 2 c)

( )mm

x+1 2

d)( )mm

x−1 2

32. A converging lens of focal length 'f ' is placed at a distance 0.3 m from an object to produce an image on a screen 0.9 m from the lens. Withthe object and the screen are in the same positions, an image of the object could also be produced on the screen by placing a converginglens of focal lengtha) f at a distance 0.1 m from the screen b) f at a distance 0.3 m from the screenc) 3f at a distance 0.3 m from the screen d) 3f at a distance 0.1 m from the screen

33. A ray of light falls on the surface of a spherical paper weight making an angle α with the normal and is refracted in the medium at an angleβ . The angle of deviation of the emergent ray from the direction of the incident ray is

a) )( β−α b) )(2 β−α c) 2/)( β−α d) )( α−β

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34. A person can not see the objects clearly placed at distances more than 40 cm. He is advised to use lens of powera) - 2.5 D b) + 2.5 D c) - 6.25 D d) + 1.5 D

35. A double convex lens of focal length 6 cm is made of glass of refractive index 1.5. The radius of curvature of one surface is double that ofthe other surface. The value of small radius of curvature isa) 6 cm b) 4.5 cm c) 9 cm d) 4 cm

36. A parallel beam of monochromatic light is incident on one face of an equilateral prism, the angle of incident being 55°. The angle ofemergence of the beam from the other face is 46°. The angle of minimum deviation isa) < 41° b) equal to 41° c) > 41° d) °≥ 41

37. A prism has a refractive angle of 60°. When placed in the position of minimum deviation, it produces a deviation of 30°. Then the angle ofincidences isa) 30° b) 45° c) 15° d) 60°.

38. A thin prism P1 with angle 4° and made from glass of refractive index 1.54 is combined with another prism P2 made from glass of refractiveindex 1.72 to produce dispersion without deviation. The angle of prism P2 is

a) 5.33° b) 4° c) 3° d) 2.6°39. In a simple microscope, if the final image is located at infinity then its magnifying power is

a) 25 / f b) 25 / D c) f / 25 d) { 1 + ( 25 / f )}

40. In a simple microscope, if the final image is located at 25 cm from the eye placed closed to the lens, then magnifying power isa) 25 / f b) { 1 + ( 25 / f )} c) f / 25 d) {( f / 25 ) + 1}

41. Magnifying power of an astronomical telescope for normal vision with usual notation is

a) − f f e0 / b) − ×f f e0 c) − f fe / 0 d) − +f fe0

42. The length of an astronomical telescope for normal vision is

a) f f e0 × b) f f e0 / c) f f e0 + d) f f e0 −

43. The magnifying power of a telescope is 9. When it is adjusted for parallel rays, the distance between the objective and the eyepiece is foundto be 20 cm. The focal length of lenses area) 18 cm, 2 cm b) 11 cm, 9 cm c) 10 cm, 10 cm d) 15 cm, 5 cm

44. If an astronomical telescope has objective and eyepiece of focal lengths 200 cm and 4 cm respectively, then the magnifying power of thetelescope for normal vision is

a) 42 b) 50 c) 58 d) 204

Answers

1. a 2. a 3. d 4. c 5. b 6. c7. d 8. b 9. a 10. a 11. b 12. b13. c 14. b 15. c 16. b 17. c 18. d19. c 20. b 21. d 22. b 23. a 24. b25. c 26. b 27. b 28. d 29. c 30. d31. a 32. b 33. b 34. a 35. b 36. a37. b 38. c 39. a 40. b 41. a 42. c43. a 44. b

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GRAVITATION

1. Choose the wrong statementa) weight of a body is greater at the poles and less at equatorb) weight of the body is greater in planes and less on hill topsc) weight of a body on the moon is less than that on the earth and is more on sund) none of the above.

2. Which of the following is the evidence to show that there must be a force acting on earth and directed towards the sun ?a) deviation of the falling bodies towards east b) revolution of the earth round the sunc) phenomenon of day and night d) apparent motion of sun round the earth.

3. If the radius of earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth's surfacewoulda) decrease b) remains unchanged c) increase d) decrease by 2%

4. In planetary motiona) the angular speed remains constantb) the total angular momentum remains constantc) the linear speed remains constantd) neither the angular momentum nor angular speed remains constant.

5. Newton's law of gravitation is universal becausea) it is always attractiveb) it acts on all heavenly bodies and particlesc) it acts on all the masses at all the distances and is not affected by the mediumd) none of the above

6. Consider the earth to be a homogeneous sphere. Scientist A goes deep down in a mine and scientist B goes high up in a balloon. Thegravitational field measured bya) A goes on decreasing and that by B goes on increasingb) B goes on decreasing and that by A goes on increasing.c) each remains unchanged.d) each goes on decreasing.

7. The tidal waves in the sea are primarily due toa) the atmospheric effect of the earthb) the gravitational effect of venus on the earth.c) the gravitational effect of the sun on the earthd) the gravitational effect of the moon on the earth.

8. If a satellite is orbiting the earth very close to its surface, then the orbital velocity does not depend ona) the mass of the satellite b) the mass of earth c) the orbital radius d) only of the above

9. There is no atmosphere on the moon becausea) it is closer to the earth b) it revolves round the earthc) it gets light from the sund) the escape velocity of gas molecules is lesser than their root mean square velocity

10. A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy isa) positive b) negativec) zero d) may be positive or negative depending upon its initial velocity

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11. If the earth is at one fourth of its present distance from the sun, the duration of the year will bea) half the present year b) one-eight the present year c) one fourth the present year d) one sixth the present year

12. The planet mercury is revolving in an elliptical orbit around the sun as shown in figure.The kinetic energy of mercury will be greatest at

a) A b) B

c) C d) D

13. An instrument is released from an artificial earth-satellite by simply detaching it from the outer wall of the satellite. The packagea) will shoot forward in the same orbit with double the velocity of the satellite.b) will go to the outer space and will get lostc) will fall to the earth belowd) will continue moving along with the satellite into the same orbit and with the same velocity.

14. The escape velocity from a planet of mass M and radius R is given by

a)2G MR b) 2 G M

R c)2M RG d) 2

RG M

15. An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R is the radius of the earth and g isacceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

a)g RR h

2

+b) g R c)

g RR h+ d)

g RR h

2

+FHGIKJ

16. The time period of a satellite in a circular orbit of radius R is T, the period of another satellite in a circular orbit of radius 4R isa) 4T b) T/4 c) 8T d) T/8.

17. A body starts from rest from a point at a distance R0 from the centre of the earth. The velocity acquired by the body when it reaches thesurface of the earth will be ( R represents radius of the earth ).

a) 2 1 1

0

G MR R−FHG

IKJ b) 2 1 1

0

G MR R−FHG

IKJ c) G M

R R1 1

0

−FHG

IKJ d) 2 1 1

0

G MR R−FHG

IKJ

18. A planet moves around the sun. At a point P, it is closest from the sun at a distance d1 and has a speed v1. At another point Q, when it isfarthest from the sun at a distance d2 , its sped will be

a) d v d12

1 22/ b) d v d2 1 1/ c) d v d1 1 2/ d) d v d2

21 1

2/

19. If g be the acceleration due to gravity at the earth's surface, the gain in the potential energy of an object of mass m raised from the surfaceof the earth to a height equal to the radius R of the earth is

a) ( 1/2 ) mg R b) 2mg R c) mg R d) ( 1/4 ) mg R

20. If the change in the value of g at the height h above the surface of the earth is the same as at a depth x below it, then ( both x and h beingmuch smaller than the radius of the earth )a) x = h b) x = 2h c) x = h/2 d) x = h2

21. The ratio of the radius of a planet X to that of planet Y is r. The ratio of acceleration due to gravity on the planets is a. The ratio of the escapevelocity from the two planets is

a) a r b) r a/ c) ra d) a r/

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22. Two planets or radii r1 and r2 are made from the same material. The ratio of the acceleration of gravity g1 / g2 at the surfaces of the two planetsis

a) r r1 2/ b) r r2 1/ c) ( / )r r1 22 d) ( / )r r2 1

2

23. A spherical planet far out in space has a mass M0 and diameter D0. A particle of mass m falling freely near the surface of this planet willexperience an acceleration due to gravity which is equal to

a) G M D0 02/ b) 4 0 0

2m G M D/ c) 4 0 02G M D/ d) Gm M D0 0

2/

24. The figure shows the motion of a planet around the sun in an elliptical orbit with sun at the focus. Theshaded areas can be assumed to be equal.If t1 and t2 represent the time taken for the planet to movefrom A to B and C to D respectively, then

a) t t1 2< b) t t1 2>

c) t t1 2= d) none of these

25. In a gravitational field, a body at a given position hasa) binding energy which increase as its speed increases b) binding energy which is independent of its speedc) zero binding energy when it is at rest d) maximum binding energy when it is at rest

26. Two satellites A and B, the ratio of whose masses is 3 : 1 are in the circular orbits of radii r and 4r, then the ratio of total mechanical energyof A to that of B isa) 1/3 b) 3 c) 3/4 d) 12

27. Assuming that the earth is spherical and of radius R, gravitational acceleration on its surface = g and mass m, then its mean density is

a)3

4gG Rπ b)

43πG Rg c)

43

2π GRg d)

34 2

gG Rπ

28. The weight of a body at earth's surface is W. At a depth half way to the centre of the earth it will be ( assuming uniform density in earth )a) W b) W/2 c) W/4 d) W/8

29. The escape velocity from the earth's surface is 11 km/sec. A certain planet has a radius twice that of the earth but its mean density is thesame as that of the earth. The value of the escape velocity from this planet would be :a) 22 km/sec b) 11 km/sec c) 5.5 km/sec d) 16.5 km/sec

30. A planet is moving in an elliptical orbit around the sun. If T, V, E and L stand respectively for its kinetic energy, gravitational potential energy,total energy and magnitude of angular momentum about the centre of force, which of the following are correct ?a) T is conserved b) V is always positivec) E is always negative d) L is conserved but direction of vector L changes continuously

Answers

1. d 2. b 3. c 4. b 5. c 6. d7. d 8. a 9. d 10. b 11. b 12. a13. d 14. a 15. d 16. c 17. b 18. c19. a 20. b 21. c 22. a 23. c 24. c25. d 26. d 27. a 28. b 29. a 30. c

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MOTION IN ONE AND TWO DIMENSIONS

1. A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the totaltime elapsed is t, the maximum velocity acquired by the car is given by

a) α βαβ

2 2+FHG

IKJ t b) α β

αβ

2 2−FHG

IKJ t c) α β

αβ+FHGIKJ t d)

αβα β+FHGIKJ t

2. The numerical ratio of displacement to distance is

a) always < 1 b) always = 1 c) always > 1 d) always ≤ 1

3. A person travels a straight road for the first half time with a velocity v1 and the second half time with a velocity v2. Then the mean velocityv is given by

a) v v v=

+1 2

2b)

2 1 1

1 2v v v= + c) v v v= 1 2 d) v v

v= 2

1

4. A passenger travels along the straight road for half the distance with velocity v1 and the remaining half distance with velocity v2. Thenaverage velocity is given by

a) v1 v2 b) v v22

12/ (c) ( ) /v v1 2 2+ d) 2 1 2 1 2v v v v/ ( )+

5. The displacement time graph for the two particles A and B are straight lines inclined at angles of 30° and 60° with the time axis. The ratioof the velocities v vA B: will be

(a) 1 : 2 b) 1 : 3 c) 3 : 1 d) 1 : 3

6. The displacement of a particle as a function of time is shown in figure. The figure indicates that

a) the particle starts with a certain velocity, but the motion is retarded and finally the particle stops.b) the velocity of the particle is constant throughoutc) the acceleration of the particle is constant throughoutd) the particle starts with a constant velocity, the motion is accelerated and finally the particle moves with another constant velocity.

7. A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the nth sec to the distance covered inn sec is

a)2 1

2n n− b)

1 12n n− c)

2 12n n− d) 2n

1n1−

8. The velocity time graph of a body is shown in figure. It amplies that at point B

a) the force is zero b) there is a force towards motionc) there is a force which opposes motion d) none of the above

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9. The velocity-time graph of a linear motion is shown below. The displacement from the origin after 8 seconds is

0 1 2 3 4 5 6 7 8 t

v (m/sec.)

(in sec.)-2

+2

+4

-4

a) 18 metres b) 16 metres c) 8 metres d) 6 metres

10. A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises isa) equal to time b) less than the time of fallc) greater than the time of fall d) twice the time of fall

11. Two bodies of different masses ma and mb are dropped from two different heights a and b. The ratio of time taken by the two to drop throughthese distance is

a) a : b b) a2 : b2 c) a b: d) M M b aa b/ : /

12. A ball is thrown vertically upward. Which of the following graph/graphs represents velocity-time graph of ball during its flight, ionoring airresistance?

v

t

(a)

v

t

(b)

v

t

(c)

v

t

(d)

13. A hydrogen balloon released on the moon willa) climb with an declaration 9.8 × 6 m/sec2 b) climb with an acceleration 9.8/6 m/sec2

c) neither climb nor fall d) fall with an acceleration 9.8/6 m/sec2

14. One body is dropped while a second body is thrown downward with an initial velocity of 1m/sec simultaneously. The separation betweenthese is 18 metres after a timea) 18 sec b) 9 sec c) 4.5 sec d) 36 sec

15. The distance travelled by a body falling from rest in the first, second and third seconds are in the ratioa) 1 : 2 : 3 b) 1 : 3 : 5 c) 1 : 4 : 9 d) none of these

16. A balloon is going vertically upwards with velocity 12 m/s. When it is at a height of 65 m above the ground, it gently releases a stone. Inhow much time the stone will reach the ground ? Take g = 10 m/s2

a) 13 sec b) 5 sec c) 6.5 sec d) 10 sec

17. A stone is dropped into a well 44.1 m deep. After how much time, the sound will be heard if the velocity of sound is 330 m/sa) 6 sec b) 3.13 sec c) 6.26 sec d) 1.56 sec

18. A boy is throwing balls into the air, throwing one whenever the previous one is at its highest point. How high do the balls rise if he throwstwice a second ?a) 2.45 m b) 1.225 m c) 19.6 m d) 4.9 m

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19. A stone is thrown vertically upward with an initial velocity u from the top of a tower, reaches the ground with a velocity 3u. The height of the toweris

a)3 2ug b)

4 2ug c)

6 2ug d)

9 2ug

20. The angle of projection, at which the horizontal range and maximum height of projectile are equal isa) 45° b) θ = tan-1 ( 0.25 ) c) θ = tan-1 4 d) 60°

21. An aeroplane is moving with a velocity u. It drops a packet from a height h. The time t taken by the packet in reaching the ground will be

a)2ghFHGIKJ b)

2uhFHGIKJ c)

hg2FHGIKJ d)

2hgFHGIKJ

22. At the top of the trajectory of a projectile, the directions of its velocity and acceleration area) perpendicular to each other b) parallel to each otherc) inclined to each other at an angle of 45° d) anti-parallel to each other

23. A passenger in a train drops a ball from the window of a train running at an acceleration 'a'. A pedstrain, on the ground, by the side of therails, observes the ball falling along

a) a vertical with an acceleration g a2 2+ b) a vertical with an acceleration g a2 2−

c) a parabola with an acceleration g a2 2+ d) a parabola with an acceleration 'g'

24. The co-ordinates of a moving particle at any time t are given by x = c t2 and y = b t2. The speed of the particle is given by

a) 2 t c b( )+ b) ( )222 bct − c) ( )22 bct + d) ( )222 bct +

25. A particle moves in a plane with a constant acceleration in a direction different from the initial velocity. The path of the particle isa) straight line b) arc of a circle c) parabola d) ellipse

26. The maximum range of a gun on horizontal terrain is 16 km. If g = 10 m/sec2, the muzzle velocity of the shell must be

a) 400 m/sec b) 160 10 m/sec c) 1600 m/sec d) 200 2 m/sec

27. A gun fires two bullets at 60° and 30° with horizontal. The bullets strike at same horizontal distance. The ratio of maximum height for thetwo bullets is in the ratioa) 2 : 1 b) 3 : 1 c) 4 : 1 d) 1 : 1

28. A large number of bullets are fired in all directions with the same speed v. What is the maximum area on the ground on which these bulletswill spread ?

a)πv

g

2

b)πvg

4

2 c) π22

2

vg d)

π2 4

2

vg

29. What happens to the centripetal acceleration of a revolving body if you double the orbital speed v and halve the angular velocity w ?a) the centripetal acceleration remains unchanged b) the centripetal acceleration is halved.c) the centripetal acceleration is doubled. d) the centripetal acceleration is quadrupled.

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30. A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at the rate of 'a' metre/sec2, then the resultantacceleration will be

a)vr

a2

22−

RSTUVW b)

vr

a4

22+

RSTUVW c)

vr

a4

22−

RSTUVW d)

vr

a2

22+

RSTUVW

31. A engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last compartment with velocity v. Themiddle point of the train passes past the same pole with a velocity of

a)2

vu +b)

2

22 vu +c)

2

22 vu +d)

2

22 uv −

32. An elevator in which a man is standing is moving upwards with a speed of 10 m/sec. If the man drops a coin from a height of 2.45 metre,

it reaches the floor of the elevator after a time )m/sec9.8(g 2=

a) s2 b) s2/1 c) s2 d) s2/1

33. A projectile is projected with a kinetic energy K. Its range is R. It will have the minimum kinetic energy, after covering a horizontal distanceequal toa) 0.25 R b) 0.5 R c) 0.75 R d) 1.0 R

34. If the range of a gun which fires a shell with muzzle speed v is R, then the angle of elevation of the gun is

a)

Rgv2

1cos b)

21cos

vRg

c)

Rgv2

1sin21

d)

21sin

21

vgR

Answers

1. d 2. d 3. a 4. d 5. d 6. a7. a 8. c 9. d 10. b 11. c 12. a13. d 14. a 15. b 16. b 17. b 18. b19. b 20. c 21. d 22. a 23. d 24. d25. c 26. a 27. b 28. b 29. a 30. b31. c 32. b 33. b 34. d

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PARTICLE DYNAMICS

1. Inertia is that property of a body by virtue of which the body isa) unable to change by itself the state of rest b) unable to change by itself the state of uniform motionc) unable to change by itself the direction of motion d) unable to change by itself the state of rest or of uniform linear motion

2. A block m slides down a smooth inclined plane of inclination θ with horizontal, when released from the top in time t. Another block fallsfreely from the same point and strikes the ground in time t/2. The value of θa) 30° b) 45° c) 60° d) none of these

3. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope,the force exerted by the rope on the block will bea) P b) P m / (M + m) c) P M / (M + m) d) P m / (M - m)

4. The mechanical advantage for a system of pulleys is four. The force needed to lift a mass of 100 kg will bea) 20 kg wt b) 25 kg wt c) 5 kg wt d) 15 kg wt

5. Three equal weights A, B, C of mass 2 kg each are hanging on a string passing over a fixed frictionlesspulley as shown in the figure. The tension in the string connecting weights B and C is

a) zero b) 13 newtonc) 3.3 newton d) 19.6 newton

6. The engines of a jet aircraft apply a thrust force of 105 N during take off and cause the plane to attain a velocity of 1 km/sec in 10 seconds.The mass of the plane isa) 102 kg b) 103 kg c) 104 kg d) 105 kg

7. A cracker rocket is ejecting 0.05 kg of gases per second at a velocity of 400 m/sec. The accelerating force on the rocket isa) 20 dynes b) 20 newtons c) 20 kilogram weight d) none of the above

8. The linear momentum P of a body varies with time and is given by the equation P = x + yt2 where x and y are constants. The net force actingon the body for a one dimensional motion is proportional to

a) t2 b) a constant c)1t d) t

9. A body of mass 2 kg is sliding with a constant velocity of 4 m/sec on a frictionless horizontal table. The force required to keep the bodymoving with the same velocity isa) 8 newton b) zero c) 2 × 104 newton d) 1/2 newton.

10. The masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 newtons acts on the 20kg mass. At the instant shown the 10 kg mass has acceleration 12 m/sec2. What is the acceleration of 20 kg mass ?

N

a) 12 m/sec2 b) 4 m/sec2 c) 10 m/sec2 d) zero11. A boy sitting on the top most berth in the compartment of a train which is moving with a constant velocity, drops an apple aiming at the open

hand of his brother sitting vertically below his hands at a distance of about 2 metre. The apple will falla) precisely on the hand of his brother.b) slightly away from the hand of his brother in the direction of motion of the train.c) slightly away from the hand of his brother in the direction opposite to the direction of motion of the train.d) none of the above.

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12. A body floats in a liquid contained in a beaker. If the whole system as shown in figure falls freely under gravity, then the up thrust on thebody due to liquid isa) zerob) equal to the weight of liquid displacedc) equal to the weight of the body in aird) equal to the weight of the immersed portion of the body

13. Two blocks of masses 2 kg and 1 kg are placed on a smooth horizontal table in contact with each other. A horizontal force of 3 newton isapplied on the first so that the block moves with a constant acceleration. The force between the blocks would bea) 3 newton b) 2 newton c) 1 newton d) zero

14. The elevator shown in figure is descending with an acceleration of 2 m/s2.The mass of the block A = 0.5 kg. The force exerted by the block Aand on block B is

a) 2 N b) 4 N

c) 6 N d) 8 N

15. A constant force F = m2 g/2 is applied on the block of mass m1 as shown in figure. The string and the pulley are light and the surface of thetable is smooth. The acceleration of m1 is

a) ( )212

2 mmgm+ towards right b)

m gm m

2

1 22 ( )− towards left

c)m gm m

2

2 12 ( )− towards right d)m gm m

2

2 12 ( )− towards left

16. Consider the system shown in figure. The pulley and the string are light and all the surfaces are frictionless. The tension in the string is(take g =10 m/s2 )

a) 0 N b) 1 N c) 2 N d) 5 N

17. An impulse is supplied to a moving object with the force at an angle θ =30° as shown. The angle between the impulse vector and thechange in momentum vector is

a) 120° b) 0° c) 60° d) 240°

18. A lift is moving downwards with an acceleration equal to the acceleration due to gravity. A body of mass M kept on the floor of the lift ispulled horizontally. If the co-efficient of friction is m, then the frictional resistance offered by the body isa) µ M g b) M g c) zero d) 2 µM g

19. If in the above question, the lift is moving upwards with a uniform velocity then the frictional resistance offered by the body isa) zero b) M g c) m M g d) 2 m M g

20. A block of mass 2 kg rests on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between theblock and the plane is 0.7. The frictional force on the block is

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a) 9.8 N b) 0.7 × 9.8 × 3 N c) 9.8 × 3 N d) 0.7 × 9.8 N.

21. Two masses A and B of 10 kg and 5 kg respectively are connected with a string passing over africtionless pulley fixed at the corner of a table as shown in figure. The coefficient of friction of Awith the table is 0.2. The minimum mass of C that may be placed on A to prevent it from movingis equal toa) 15 kg b) 10 kgc) 5 kg d) 0 kg

22. Two blocks are connected over a massless pulley as shown in figure. The mass of block A is10 kg and the coefficient of kinetic friction is 0.2. Block A slides down the incline at constantspeed. The mass of block B in kg is

a) 3.5 b) 3.3c) 3.0 d) 2.5

23. A 60 kg body is pushed with just enough force to start it moving across a floor and the same force continues to act afterwards. The co-efficients of static and sliding friction are 0.5 and 0.4 respectively. The acceleration of the body isa) 6 m/sec2 b) 4.9 m/sec2 c) 3.92 m/sec2 d) 1 m/sec2

24. A body moves along circular path of radius 10 m and the coefficient of friction is 0.5. What should be its maximum angular velocity in rad/sec if it is not to slip from the surface. g = 9.8 m/sec2.a) 10 b) 5 c) 0.1 d) 0.7

25. Consider a car moving along a straight horizontal road with a speed of 72 km/hr. If the coefficient of static friction between the tires and theroad is 0.5, the shortest distance in which the car can be stopped is [ Take g = 10 ms-2 ]a) 30 m b) 40 m c) 72 m d) 20 m

26. A heavy box is thrust across a rough floor with an initial speed of 4 m/sec. It stops moving after 8 seconds. If the resisting force of frictionwas on an average 10 newton, the mass of the box in kg isa) 40 b) 20 c) 5 d) 2.5

27. A car turns a corner on a slippery road at a constant speed of 10 m/sec. If the co-efficient of friction is 0.5, the minimum radius of the arc inmetres in which the car turns isa) 20 b) 10 c) 5 d) 4

28. A person carries a hammer on his shoulder and holds the other end of its light handle in his hand. Let y be the distance between his handand the point of support. If the person increases y, the pressure on his hand willa) increase b) decrease c) remain same d) none of these

29. A string of length L and mass M is lying on a horizontal table. A force F is applied at one of its ends. Tension in the string at a distance y fromthe end at which the force is applied is

a) zero b) F c)LyLF )( −

d)MyLF )( −

30. In the system shown in the adjoining figure, the acceleration of the 1 kg mass is

a) g/4 downwards b) g/4 upwards c) g/2 downwards d) g/2 upwards

B

A

30°

kg1

kg4

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31. In the figure, a block of weight 60 N is placed on a rough surface. The coefficient of friction between theblock and the surfaces is 0.5. What should be the weight W such that the block does not slip in thesurface ?a) 60 N b) N260/

c) 30 N d) N20/3

32. A particle is projected up along the slope of a rough plane inclined at an angle of 45° with thehorizontal. If the coefficient of friction is 1/2, its retardation is

a) g2 b) 2g

c)

211

2g

d)

+

211

2g

33. The minimum acceleration that must be imparted to the cart in the figure so that the block Awill not fall (given µ is the coefficient of friction between the surfaces of block and cart) isgiven by

a) gµ b) µ/g

c) µ/g d) g/µ34. A block moves down a smooth inclined plane of inclination θ . Its velocity on reaching the bottom is v. If it slides down a rough inclined plane

of same inclination, its velocity on reaching the bottom is nv / , where n is a number greater than one. The coefficient of friction µ is givenby

a)

−θ=µ 2

11tann

b)

−θ=µ 2

11cotn

c) 211tann

−θ=µ d) 211cotn

−θ=µ

°45A

2T

1TN60

W

C

A

Answers

1. d 2. a 3. c 4. b 5. b 6. b7. b 8. d 9. b 10. b 11. a 12. a13. c 14. b 15. a 16. d 17. b 18. c19. c 20. a 21. a 22. b 23. d 24. d25. b 26. b 27. a 28. b 29. c 30. d31. c 32. d 33. b 34. a

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ROTATION DYNAMICS AND ANGULAR MOMENTUM

1. When a steady torque is acting on a body, the bodya) continues in its state of rest or uniform motion along a straight lineb) gets linear acceleration c) gets angular accelerationd) rotates at a constant speed

2. A dancer on ice spins faster when she folds her arms. This is due toa) increase in energy and increase in angular momentumb) decrease in friction at the skatesc) constant angular momentum and decrease in Moment of Inertiad) increase in energy and decrease in angular momentum

3. A man is standing on a table rotating with an angular speed ω . He is holding two equal masses at arm's length. Without moving his arms,he just drops the two masses on the table. How will his angular speed change ?a) it will be less than ω b) it will be more than ωc) it will remain equal toωd) may be less than, greater than or equal to ω depending on the quantity of masses.

4. A hollow cylinder and a solid cylinder having the same mass and same diameter are released from rest simultaneously from the top of aninclined plane. Which will reach the bottom firsta) the solid cylinder b) the hollow cylinderc) both will reach the bottom together d) the one having greater density

5. A body of mass m slides down an incline and reaches the bottom with a velocity v. If the same mass were in the form of a ring which rollsdown this incline, the velocity of the ring at bottom would have been

a) v b) 2 v c)12v d) 2

5 v6. A particle of mass m is moving in a plane along a circular path of radius r. Its angular momentum about the axis of rotation is L. The

centripetal force acting on the particle is

a) L2 / mr b) L2 mr c) L2 / mr3 d) L2 / mr2

7. A disc of radius R rotating about its axis, has a moment of inertia I about that axis. When it is rotating about that axis at a constant angularvelocity 'ω ' a heavy particle of mass m is placed gently at the rim of the disc. The resulting angular velocity of the system is

a) ω b) ωI ( I + mR ) c) ( I + mR )/ω d) ωI /( I + mR2 )

8. A thin circular ring of mass M and radius r is rotating about an axis passing through its centre and perpendicular to its plane with a constantangular velocity ω . Two objects, each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotateswith angular velocity

a)ω ( )M mM m

−+22

b) ω M M m( )− c)ω ( )M m

M+ 2

d)ω MM m+ 2

9. A solid iron sphere A rolls down an inclined plane, while an identical sphere B slides down the plane in a frictionless manner. At the bottomof the inclined plane, the total kinetic energy of sphere A isa) less than that of B b) equal to that of B c) more than that of B d) sometimes more and sometimes less

10. A solid cylinder of mass M and radius R rolls down an inclined plane without slipping from height h. The speed of its centre of mass whenit reaches the bottom is

a) ( )2gh b) 43 gh c) 3

4 gh d) ( / )4 g h

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11. The angular velocity of a body changes from 1ω to 2ω without applying torque but by changing radius of gyration. The ratio of initial radius ofgyration of the final radius of gyration is

a) ω ω2 1: b) ω ω22

12: c) ω ω2 1: d) 1 12 1/ : /ω ω

12. A circular disc rotates in a vertical plane about a fixed horizontal axis which passes through a point X on the circumference of the disc.When the centre of the disc moves with speed V, the speed of the opposite end of the diameter through X is

a) 2 V b) 2 V c) V d) V/2

13. Two circular discs A and B of equal masses and thickness are made of metals with densities dA and dB ( dA > dB ). If their moments of inertiaabout an axis passing through the centre and normal to the circular faces be IA and IB, then

a) I IA B= b) I IA B> c) I IA B< d) I IA B≥

14. Two bodies with moment of inertias I1 and I2 ( )I I1 2> have equal angular momenta. If K.E. of rotation are E1 and E2 , then

a) E E1 2= b) E E1 2> c) E E1 2< d) E E1 2≥

15. A disc rolls over a horizontal floor without slipping with a linear speed of 5 cm/sec. Then the linear speed of a particle on its rim, with respectto the floor, when it is in its highest position isa) 10 cm/sec b) 5 cm/sec c) 2.5 cm/sec d) 0

16. Without weighing, how can you distinguish between the two identical balls of same material, but one being solid and the other one beinghollowa) by rolling them down on inclined plane, b) by determing their moment of inertia about the centre,c) by spinning them by equal torque, d) all the above

17. A mass M is moving with a constant velocity parallel to x-axis. Its angular momentum with respect to origin isa) zero b) constant c) goes on increasing d) goes on decreasing

18. A wheel of moment of inertia 5 × 10-3 kg-metre2 is making 20 revolutions per second. It is stopped in 20 seconds, then angular retardationisa) π radian/sec2 b) 2π radian/sec2 c) 4π radian/sec2 d) 8π radian/sec2

19. A solid spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is -

a) 2/5 b) 2/7 c) 3/5 d) 3/7

20. An inclined plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping hasa linear acceleration equal toa) g/3 b) 2g/3 c) 5g/7 d) 5g/14

21. A constant torque acting on a uniform circular wheel changes its angular momentum from A0 to 4A0 in 4 seconds. The magnitude of thistorque is

a) 3A0 / 4 b) A0 c) 4A0 d) 12A0

22. A particle of mass m = 5 is moving with a uniform speed v = 3 2 in the XOY plane along the line Y = X + 4. The magnitude of theangular momentum about origin is

a) zero b) 60 units c) 7.5 units d) 40 2

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23. A particle of mass M and radius of gyration K is rotating with angular acceleration α . The torque acting on the particle is

a) α2Mk21

b) MK2α c) MK2 / α d) ( MK2 α 2 / 4 )

24. K.E. (E) and the angular momentum L of a rigid body are related to each other by the relation( I = moment of inertia )

a) LEI

=2

2b) E IL= 2 c) E I L2 2= / d) E L I= 2 2/

25. Mass is whirled in a circular path with a constant angular velocity and its angular momentum is L. If the string is now halved keeping theangular velocity same, the angular momentum is

a) L/4 b) L c) 2L d) L/2

26. A small hole is made in a disc ( Mass M, radius R ) at a distance R/4 from centre. The disc is supported on horizontal peg through this hole.The moment of inertia of disc about horizontal peg is

a)Mr2

2b)516

2MRc)916

2MRd)54

2MR

27. Moment of inertia of uniform circular disc about a diameter is I . Its moment of inertia about an axis perpendicular to its plane and passingthrough a point on its rim will bea) 5 I b) 3 I c) 6 I d) 4 I

28. A particle performs uniform circular motion with an angular momentum L. If the frequency of particle's motion is doubled and its kineticenergy halved, the angular momentum becomesa) 2 L b) 4 L c) L / 2 d) L / 4

29. A particle of mass m is projected with a velocity v making an angle of 45° with the horizontal. The magnitude of angular momentum of theprojectile about an axis of projection when the particle is at maximum height h is

a) 0 b) mv g3 4 2/ c) mv g2 2/ d) gmv 22/3

30. The moment of inertia of a thin square plate ABCD ( shown below in the figure ) of uniform thickness about an axis passing through thecentre O and perpendicular to the plane of plate is (where 4321 IandI,I,I are moments of inertia about axes 1, 2, 3 and 4 respectivelywhich are in the plane of paper).a) I I1 2+ b) ( I I3 4+ )/2 c) I I1 3+ d) I I I I1 2 3 4+ + +

31. A solid, homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During thiskind of motion of the spherea) total kinetic energy is conservedb) the angular momentum of the sphere about the point of contact with the plane is conservedc) only the rotational kinetic energy about the centre of mass is conservedd) angular momentum about the centre of mass is conserved.

32. A solid sphere of mass 2 kg and radius 5 cm rolls without slipping along a horizontal plane. The velocity of its centre of mass is 10 cm s-1.The kinetic energy of the sphere isa) 0.07 J b) 0.014 J c) 0.025 J d) 1.25 J

33. If 1I is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass, and 2I is themoment of inertia of the ring formed by bending the rod, then

a) I I1 2 1 1: := b) I I1 22 3: := π c) I I1 2 4: := π d) I I1 2 3 5: :=

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34. A thin uniform heavy rod of length l hangs from a horizontal axis passing through one end. The initial angular velocity ω that must be impartedto it to rotate it through 90° is

a) g l/ b) 3g l/ c) 2g l/ d) 6g l/

35. An initial momentum is imparted to a homogeneous cylinder, as a result of which it begins to roll without slipping up an inclined plan

e at a speed of 14 −= msvo . The plane makes an angle °=θ 30 with the horizontal. What height h will the cylinder rise to ? )m/s10(g 2=a) 0.8 m b) 1.2 m c) 1.0 m d) 1.6 m

Answers

1. c 2. c 3. c 4. a 5. c 6. c7. d 8. d 9. b 10. b 11. c 12. a13. c 14. c 15. a 16. d 17. b 18. b19. b 20. d 21. a 22. b 23. b 24. d25. a 26. c 27. b 28. d 29. b 30. a31. b 32. b 33. b 34. b 35. b

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SIMPLE HARMONIC MOTION

1. A clock 'S' is based on oscillations of a spring and another clock 'P' is based on pendulum motion. Both clocks run at the same rate on earth.On a planet having the same density as earth, but twice the radiusa) S will run faster than P, b) P will runs faster than S,c) they will both run at the same rate as on the earth, d) they will both run at equal rates, but not the same as on theearth.

2. The mass and diameter of a planet are twice those of earth. The period of oscillation of pendulum on this planet will be ( if it is a second'spendulum on earth )

a) 1 2/ second b) 2 second, c) 2 second d) ( 1/2 ) second.

3. When particle oscillates simple harmonically, its kinetic energy vary periodically. If frequency of the particle is n, the frequency of the kineticenergy isa) 4n b) n c) 2n d) n/2

4. A particle is vibrating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is itsenergy half potential and half kinetic ?

a) 1 cm b) 2 cm c) 3 cm d) 2 2 cm

5. A particle moves such its acceleration a is given by a = -bx, where x is the displacement from equilibrium position and b is a constant. Theperiod of oscillation is

a) 2π b b) 2π / b c) 2π / b d) 2 ( / )π b

6. A simple pendulum performs simple harmonic motion about X = 0 with an amplitude A and time period T. The speed of the pendulum at X= A/2 will be

a) πA T3 / b) πA T/ c) πA T3 2/ d) 3 2π A T/

7. The potential energy of a particle with displacement X is U (X). The motion is simple harmonic, when ( K is a positive constant )

a) U KX= − 2 2/ , b) 2/2KXU = c) U = K, d) U = KX.

8. The total energy of the body executing S.H.M. is E. Then the kinetic energy when the displacement is half of the amplitude is

a) E/2 b) E/4 c) 3E/4 d) 3 4/ . .E

9. Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants k1 and k2 respectively. If thetwo bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of M to that of N is

a) k k1 2/ b) k k1 2/ c) k k2 1/ d) k k2 1/

10. A mass m is suspended by means of two coiled springs which have the same length in unstretched condition (seefigure). Their force constants are k1 and k2 respectively. When set into vertical vibrations, the period will be

a) 21 2

πmk kFHGIKJ b) 2 1

2

π m kkFHGIKJ

RSTUVW

c) 21 2

πm

k k−FHG

IKJ d) 2

1 2

πm

k k+FHG

IKJ

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11. A spring has a certain mass suspended from it and its period for vertical oscillations is T1. The spring is now cut into two equal halves and the same

mass is suspended from one of the halves. The period of vertical oscillations is now T2. The ratio of T2/T1 is

a) 1/2 b) 1 2/ c) 2 d) 2.

12. Two masses m1 and m2 are suspended together by a massless spring of constant k. When the masses are in equilibrium, m1 is removedwithout disturbing the system. Then the angular frequency of oscillation of m2 is

a) ( / )k m1 b) ( / )k m2 c) [ / ( )]k m m1 2+ d) [ / ( )]k m m1 2

13. A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance x. Now the combinedmass will oscillate on the spring with period.

a) T mg x M m= +2π / ( ) b) T M m x mg= +2π ( ) /

c) T mg x M m= +π2

/ ( ) d) T M m mgx= +2π ( ) /

14. In arrangement given in figure, if the block of mass m is displaced, the frequency is given by

a) n k km

=−FHG

IKJ

12

1 2

πb) n k k

m=

+FHG

IKJ

12

1 2

π c) n mk k

=+FHG

IKJ

12 1 2π

d) n mk k

=−FHG

IKJ

12 1 2π

15. Two identical springs of constant k are connected in series and parallel as shown in figure. Amass m is suspended from them. The ratio of their frequencies of vertical oscillations will be

a) 2 : 1 b) 1 : 1 c) 1 : 2d) 4 : 1

16. A sphere of radius r is kept on a frictionless concave mirror of radius of curvature R. Thearrangement is kept on a horizontal table. If the sphere is displaced from its equilibrium positionand left, then it executes S.H.M. The period of oscillation will be

a) 2 14π

( ) .R rg−F

HGIKJ b)

−π

grR2 c) 2π

( )r RaFHGIKJ d) 2π R

g rFHGIKJ

17. The motion of a particle executing simple harmonic motion is given by X = 0.01 sin 100 p ( t + 0.05 ), where X is in metres and t in seconds.The time period in seconds isa) 0.01 b) 0.02 c) 0.1 d) 0.2

18. While driving around a curve of 200 m radius, an engineer notes that pendulum in the car hangs at an angle of 15° to the vertical. Thespeedometer of the car reads ( in m/sec )a) 20 b) 230 c) 23 d) 236

19. The work done in increasing the extension of a spring from 40 cm to 50 cm is 18 J. The spring constant isa) 180 N/m b) 200 N/m c) 360 N/m d) 400 N/m

20. The length of a simple pendulum is increased by 44%. What is the percentage increase in its period?a) 44% b) 20% c) 10% d) 5%

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21. An elastic string has a length a when tension in it is 4 N. Its length is b when tension is 5 N. On subjecting the string to a tension of 9 N its lengthwill be

a) a + b b) b - a c) ( 5b - 4a ) d) [(a + b)/(b - a)]

22. A block rests on a horizontal table which is executing S.H.M. in the horizontal plane with an amplitude a. If the coefficient of friction is m, theblock just stars to slip when the frequency of oscillation is

a)12π

µ gaFHGIKJ b)

µ gaFHGIKJ c)

12π µ

agFHGIKJ d)

agµFHGIKJ

23. The force acting on a particle moving along the x axis varies according to figure-

a) Stable equilibrium both at A and Bb) Unstable equilibrium at A and Bc) Stable at A and unstable at Bd) Unstable at A and stable at B

24. For a simple pendulum, the graph between 'L' and 'T' will bea) hyperbola b) parabola c) a straight line d) a curved line.

25. If a simple harmonic oscillator has got a displacement of 0.02 m and acceleration equal to 2.0 m s-2 at any time, the angular frequency ofthe oscillator is equal toa) 10 rad s-1 b) 0.1 rad s-1 c) 100 rad s-1 d) 1 rad s-1

26. A simple harmonic oscillator has an amplitude A and time period T. The time required by it to travel from x = A to xA

=2 is

a) T/6 b) T/4 c) T/3 d) T/2

27. A body of mass 10 g executes SHM with amplitude 2 cm and time period 2 s ( take 102 =π ). The energy of the particle isa) 10 J b) 10-5 J c) 2 × 10-5 J d) 4 × 10-5 J

28. The time period of second’s pendulum is 2 sec. The spherical bob which is empty from inside has a mass of 50 g. This is now replaced byanother solid bob of same radius but having a different mass of 100 g. The new time period will bea) 4 sec b) 1 sec c) 2 sec d) 8 sec

29. The periodic time of a mass suspended by a spring (force constant k) is T. If the spring is cut in three equal pieces, what will be the forceconstant of each part and what will be the periodic time if the same mass is suspended from one piece ?

a) 3/, Tk b) Tk,3 c) Tk 3,3 d) 3/,3 Tk

30. Three masses 700g, 500 g and 400g are suspended at the end of a spring as shown and are in equilibrium. When the700 g mass is removed, the system oscillates with a period of 3 second. When the 500g mass is also removed, it willoscillate with a period of

a) 1 sec b) 2 secc) 3 sec d) sec3/12

31. A simple harmonic oscillator has a period of 0.01 sec and an amplitude of 0.2 m. The magnitude of the velocity in 1ms− at the centre ofoscillation isa) 100 b) π100 c) π20 d) π40

BA x

F

g700g005g004

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32. What will be the force constant of the spring system shown in the figure ?

1k 1k

2kM

a) 21

2kk

+ b)1

21 k1

k21

+ c)

21

121

kk+ d)

+

21

11kk

33. The kinetic energy of a particle, exceuting SHM is 16 J when it is in its mean position. If the amplitude of oscillation is 25 cm and the massof the particle is 5.12 kg, the time period of its oscillation isa) sec5/π b) sec2π c) sec20π d) sec5π

34. On a smooth inclined plane, a body of mass M is attached between two springs. The other ends of the springs are fixed to firm supports.If each spring has force constant k, the period of oscillation of the body (assuming the springs as massless) is

θ

M

a) 2/1)2/(2 KMπ b) 2/1)/2(2 KMπ c) )2/sin(2 KMg θπ d) 2/1)/2(2 KMgπ

Answers1. b 2. b 3. c 4. d 5. b 6. a7. b 8. c 9. d 10. d 11. b 12. b13. b 14. b 15. c 16. b 17. b 18. c19. d 20. b 21. c 22. a 23. d 24. b25. a 26. a 27. c 28. c 29. d 30. b31. d 32. c 33. a 34. a

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THERMODYNAMICS & KINETIC THEORY OF GASES

1. Heat added to a system is equal toa) a change in its internal kinetic energy b) a change in its internal potential energyc) workdone by it d) sum of above all the three.

2. The area inside a closed curve on P-V diagram representsa) the condition of a system b) work done on the systemc) workdone in a cyclic process d) a thermodynamic process

3. In the diagrams (i) to (iv) of figure, variation of volume by changing pressure is shown. A gas is taken along the path ABCD. The change ininternal energy of the gas will be

a) positive in all the cases (i) to (iv) b) positive in cases (i), (ii) and (iii) but zero in case (iv)c) negative in cases (i), (ii) and (iii) but zero in case (iv) d) zero in all the four cases.

4. The second law of thermodynamics impliesa) whole of the heat can be converted into mechanical energy b) no heat engine can be 100% efficientc) every heat engine has an efficiency of 100% d) a refrigerator can reduce the temperature to absolute zero.

5. The maximum amount of heat that can be converted into mechanical energy in any processa) is 100% b) depends upon the temperatures of intake and exhaustc) depends upon the amount of friction present d) is the same for reversible and irreversible cycles.

6. A Carnot engine works between a source and a sink maintained at constant temperatures T1 and T2. For efficiency to be the greatest

a) T1 and T2 should be high b) T1 and T2 should be low

c) T1 should be low and T2 should be high d) T1 should be high and T2 should be low.

7. In a thermodynamic process, pressure of a fixed mass of gas is changed in such a manner that the gas release 20 joule of heat and 8 jouleof work was done on the gas. If the initial internal energy of the gas was 30 joule, then the final internal energy will bea) 2 joule b) 18 joule c) 42 joule d) 58 joule

8. During an adiabatic expansion of 2 moles of a gas, the change in internal energy was found to be equal to -100 J. The workdone during theprocess will be equal toa) zero b) -100 joule c) 200 joule d) 100 joule

9. A Carnot engine working between 300 K and 600 K has a work output of 800 J per cycle. The amount of heat energy supplied to the enginefrom the source in each cycle isa) 800 J b) 1600 J C) 3200 J d) 6400 J

10. The temperature of the sink of a Carnot engine is 27°C. If the efficiency of the engine is 25%, the temperature of the source isa) 227°C b) 327°C c) 127°C d) 27°C

11. The efficiency of a Carnot cycle is 1/6. If in reducing the temperature of sink by 65°K, the efficiency becomes 1/3. The initial and finaltemperatures between which the cycle is working are

a) C13,C52 °−° b) 217°C, 52°C c) 317°C, 52°C d) 17°C, 52°C

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12. The temperature of inside and outside of a refrigerator are 273 K and 303 K respectively. Assuming that the refrigerator cycle is reversible, forevery joule of workdone, the heat delivered to the surrounding will be nearlya) 10 J b) 20 J c) 30 J d) 50 J

13. An ideal non-atomic gas is taken round the cycle ABCDA in the P-V diagram where the coordinates ofthe points are : A ( P1, V1 ) ; B ( 2P1, V1 ) ; C ( 2P1, 2V1 ) and D ( P1, 2V1 ). The work done during thecycle is :

a) P V1 1 b) 2 1 1P V

c) 12 1 1PV d) zero

14. From what minimum height, a block of ice has to be dropped in order that it may melt completely on hitting the ground ? ( L is the latent heatof ice and J is Joule's constant )

a) mgh b) mgh / J c) JL / g d) J/Lg

15. An ideal gas is taken around the cycle ABCA as shown in P-V diagram. The net workdone by the gasduring the cycle is equal to

a) 12 P1 V1 b) 6 P1 V1

c) 3 P1 V1 d) P1 V1

16. When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy suppliedwhich increases the internal energy of the gas isa) 2 / 5 b) 3 / 5 c) 3 / 7 d) 5 / 7

17. A thermodynamical system goes from state (i) P1, V to 2P1, V. Another system goes from state (ii) P1, V to P1, 2V . Then the wokdone in thetwo cases isa) (i) zero (ii) zero b) (i) zero (ii) P1 V c) (i) P1 V (ii) zero d) (i) P1 V (ii) P1 V

18. The pressure exerted by a gas on the walls of a container is given by

a) PMVv=

13

2 b) P VMv=

13

2 c) P M v=13

2 d) P M v= 3 2

19. The absolute temperature of a gas is determinesa) the average momentum of the molecule b) the velocity of sound in thegasc) the number of molecules in the gas d) the mean square velocity ofthe molecules

20. Two vessels having equal volume contains molecular hydrogen at one atmosphere and helium at two atmospheres respectively. If bothsamples are at the same temperature, the mean velocity of hydrogen molecules is

a) equal to that of helium b) twice that of helium c) half that of helium d) 2 times that ofhelium

21. A gas at a pressure P0 is contained in a vessel. If the masses of all the molecules are halved and their velocities doubled, the resultingpressure P would be equal toa) 4 P0 b) 2 P0 c) P0 d) P0/2

22. We have a jar A filled with gas characterised by parameters P, V and T and another jar B filled with a gas with parameters 2P, V/4 and 2T,where the symbols have the usual meanings. The ratio of the number of molecules of jar A to those of jar B isa) 1 : 1 b) 1 : 2 c) 2 : 1 d) 4 : 1

B

A

4P1

P1

V1 3V1

CP

V(O,O)

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23. A gas in a container A is in thermal equilibrium with another gas (having same no.of moles) in container B. If we denote the correspondingpressures and volumes by the suffixes A and B, then which of the following statement is most likely to be true.

a) P P V VA B A B= ≠, b) P P V VA B A B≠ =, c) BBAA VPVP // = d) BBAA VPVP =

24. The speed of sound in a gas is v. The r.m.s velocity of the gas molecules is C. The ratio of v to C is

a) 3 / γ b) γ / 3 c) ( / )3 γ d) ( / )γ 3

25. Two gases are at absolute temperatures 300°K and 350°K respectively. The ratio of average kinetic energy of their molecules isa) 7 : 6 b) 6 : 7 c) 36 : 49 d) 49 : 36

26. A sealed container with negligible thermal coefficient of expansion contains helium (a monatomic gas ). When it is heated from 300 to 600 K,the average kinetic energy of the helium atom is

a) halved b) left unchanged c) doubled d) becomes 2 times.

27. A fixed mass of gas at constant pressure occupies a volume V. The gas undergoes a rise in temperature so that the root mean squarevelocity of its molecules is doubled. The new volume will be

a) V / 2 b) V / 2 c) 2V d) 4V

28. A sample of oxygen gas and a sample of H2 gas both have the same mass, the same volume and the same pressure. The ratio of theirabsolute temperature is

a) 1 : 4 b) 4 : 1 c) 1 : 16 d) 16 : 1

29. If a system is caused to change reversibly from an initial state to a final state by adiabatic means only, thena) the work done is the same for all adiabatic paths connecting the two states.b) the work done is different for different adiabatic paths connecting the two statesc) the total internal energy of the system will change according to different paths.d) there is no work done since there is no transfer of heat energy.

30. When a gas expands adiabaticallya) no energy is required for expansionb) energy is required and it comes from the wall of the container of the gasc) internal energy of the gas is used in doing workd) law of conservation of energy does not hold.

31. During an adiabatic process, the pressure P of a fixed mass of an ideal gas changes by Pδ and its volume V changes by Vδ . The valueof V/Vδ is given by

a) −δP P/ b) −γ δ. /P P c) −1γδ. PP

d) −12γδ. PP

32. The work done in an isothermal expansion of a gas depends upon(a) temperature only b) expansion ratio onlyc) both temperature and expansion ratio d) neither temperature nor expansion ratio.

33. Two samples A and B of a gas initially of the same temperature and pressure are compressed from a volume V to a volume V/2 such thatA is compressed isothermally and B adiabatically. The final pressure ofa) A is greater than that of B b) A is equal to that of Bc) A is less than that of B d) A is twice the pressure of B.

34. A monoatomic ideal gas initially at 17°C is suddenly compressed to one-eight of its original volume. The temperature after compression isa) 17°C b) 136°C c) 887°C d) none of these

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35. Four curves A, B, C and D are drawn in figure for a given amount of gas. The curves which represent adiabatic and isothermal changes are

a) C and D respectively b) D and C respectivelyc) A and B respectively d) B and A respectively

36. If a gas has 'n' degrees of freedom, the ratio of the specific heats of the gas is

a)12+ n

b) 12

+n

c) 1 1+n

d) 12

+n

37. The root mean square speed of a group of n gas molecules, having speed v1 , v2 , v3 , ...., vn is

a)1

1 2 32

nv v v vn( .... )+ + + + b)

112

22

32 2

nv v v vn( .... )+ + + +

c)1

12

22

32 2

nv v v vn( .... )+ + + + d)

( .... )v v v vn

n1 2 32+ + + +L

NMOQP

38. The pressure and density of a diatomic gas )5/7( =γ change adiabatically from ),( ρP to )','( ρP . If 32)/'( =ρρ , then )/'( PPisa) 128 b) 1/128 c) 32 d) none of the above

39. 1/2 mole of helium gas is contained in a container at S.T.P. The heat energy needed to double the pressure of the gas, keeping the volume

constant (heat capacity of the gas 11Kg3J −−= )a) 3276 J b) 1638 J c) 819 J d) 409.5 J

Answers

1. d 2. c 3. d 4. b 5. b 6. d7. b 8. d 9. b 10. c 11. a 12. a13. a 14. c 15. c 16. d 17. b 18. a19. d 20. a 21. b 22. d 23. d 24. d25. b 26. c 27. d 28. d 29. a 30. c31. c 32. c 33. c 34. c 35. c 36. d37. c 38. a 39. b

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UNIT DIMENSIONS AND ERRORS

1. One nanometre is equal toa) 109 mm b) 10-6 mm c) 10-7 mm d) 10-9 mm

2. A micron is related to centimetre asa) 1 micron = 10-8 cm b) 1 micron = 10-6 cm c) 1 micron = 10-5 cm d) 1 micron = 10-4 cm

3. The SI unit of universal gas constant (R) isa) Watt K-1 mol-1 b) N K-1 mol-1 c) J K-1 mol-1 d) erg K-1 mol-1

4. Stefan's constant has the unita) Joule metre-2 °K-4 b) kg sec-3 °K-4 c) Watt metre-2 °K-4 d) Newton metre sec-1 °K-4

5. The unit of temperature in S.I. system isa) Degree centigrade b) Degree Celsius c) Kelvin d) Degree Fahrenheit

6. Joule X sec is the unit ofa) energy b) momentum c) angular momentum d) power

7. The dimensional formula for latent heat isa) M° L2 T-2 b) M L T-2 c) M L2 T-2 d) M L2 T-1

8. The dimensional formula for r.m.s. (root mean square) velocity isa) M° L T-1 b) M° L° T-2 c) M° L° T-1 d) M L T--3

9. The dimensions of electrical conductivity area) M-1 L-3 T3 A2 b) M L3 T3 A2 c) M L3 T-3 A-2 d) M2 L3 T-3 q2

10. If C and R denote the capacity and resistance, the dimensions of CR are

a) M° L° T-1 b) M1 L° T c) M° L° T d) not expressible of MLT.

11. The dimension of universal Gravitational constant isa) M-2 b) M-1 L3 T-2 c) M-1 L-3 T-2 d) M L2 T-2

12. The dimensions of voltage in terms of MLTA area) M L2 T3A-1 b) M L2 T-3A-2 c) M L2 T-3A-1 d) M L2 T-3A1

13. E, m, J and G denote energy, mass, angular momentum and gravitational constant respectively. Then the dimension of E J2 / m5 G2 area) angle b) length c) mass d) time

14. From the equation tan rg/v2=θ , one can obtain the angle of banking θ for a cyclist taking a curve. The symbols have their usualmeanings. We can say that it isa) both dimensionally and numerically correct b) neither numerically nor dimensionally correctc) dimensionally correct only d) numerically correct only

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15. The dimensional formula for impulse is same as the dimensional formula fora) momentum b) forcec) rate of change of momentum d) torque

16. A dimensionally consistent relation for the volume V of a liquid of co-efficient of viscosity h flowing per second through a tube of radius r and lengthl and having a pressure difference p across its end is

a) V pr l= π η4 8/ b) V l p r= πη / 8 4 c) V p l r= 8 4η π/ d) V p l l r= π η / 8 4

17. The dimensions of the quantities in one (or more) of the following pairs are the same. Identify the pairsa) Torque and work b) Angular momentum and workc) Energy and Young's modulus d) Light year and wavelength

18. L, C and R represent physical quantities - inductance, capacitance and resistance respectively. The combinations which have the dimensionsof frequency are

a) 1/RC b) R/L c) 1/ LC d) C/L

19. The velocity v ( in cm/sec ) of a particle is given in terms of time t ( in sec ) by the equation, v at bt c

= ++. The dimensions of a, b and

c area b c

a) L2 T LT2

b) LT2 LT Lc) LT -2 L Td) L LT T2

20. The equation of state of some gases can be expressed as ( ) RTbVVap =−

+ 2

.Here, P is the pressure, V the volume, T the

absolute temperature, and a, b, R are constants. The dimensions of 'a' are

a) M L T5 2− b) M L T− −1 2 c) M L T0 3 0 d) M L T0 6 0

21. The number of particles is given by n D n nx x

= −−−

2 1

2 1

crossing a unit area ⊥ to X-axis in unit time, where

n1 and n2 are number of particles per unit volume for the value of x meant to x2 and x1, find dimensions of D called as diffusion constant

a) M LT0 2 b) M L T0 2 4− c) M LT0 3− d) M L T0 2 1−

22. If V denotes the potential difference across the plates of a capacitor of capacitance C, the dimensions of CV2 are

a) Not expressible in MLT b) M LT −2 c) M LT2 1− d) M L T2 2−

23. If L denotes the inductance of an inductor through which a current i is flowing, the dimensions of L i2 are

a) M L T2 2− b) Not expressible in MLT c) M LT −2 d) M L T2 2 2−

24. Error in the measurement of radius of a sphere is 1%. Then error in the measurement of volume isa) 1% b) 5% c) 3% d) 8%

25. If a physical quantity is represented by X = Ma Lb T -c and if percentage error in the measurement of M, L and T are %and%,% γβαrespectively, then total percentage error is

a) ( )%α β γa b c− + b) ( )%α β γa b c+ + c) %)cba( γ−β−α d) None of these

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26. Of the following quantities, which one has dimensions different from the remaining three ?a) Energy per unit volume b) Force per unit areac) Product of voltage and charge per unit volume d) Angular momentum per unit mass

27. A spherical body of mass m and radius r is allowed to fall in a medium of viscosity h. The time in which the velocity of the body increasesfrom zero to 0.63 times the terminal velocity (v) is called time constant (t). Dimensionally t can be represented by

a)mr 2

6πη b)6

2

π ηmrg

FHG

IKJ c)

mr v6πη d) None of these

28. The density of a cube is measured by measuring its mass and the length of its sides. If the maximum errors in the measurement of massand length are 3% and 2% respectively, then the maximum error in the measurement of the density isa) 9% b) 7% c) 5% d) 1%

29. If the value of r is 10.845 ohm and the value of current is 3.23 amp., the potential is 35.02935 its value in significant number would bea) 3.50 V b) 35.0 V c) 35.029 V d) 35.030 V

30. The least count of a stop watch is 1/5 second. The time of 20 oscillations of a pendulum is measured to be 25 seconds. The percentageerror in the measurement of time will bea) 0.1 % b) 0.8 % c) 1.8 % d) 8 %

31. In a Vernier calliper, N divisions of vernier scale coincides with N - 1 divisions of main scale (in which length of one division is 1 mm ). Theleast count of the instrument should bea) N b) N - 1 c) 1/ N d) 1/N - 1

32. An experiment measures quantities a, b, c and then x is calculated as x ab c= 2 3/ . If the percentage errors in a, b, c are ± ±1%, 3%and ±2% respectively, the percentage error in x can be

a) ± 13% b) ± 7% c) ± 4% d) ± 1%

33. The dimensional formula for coefficient of viscosity is

a) M L T2 2− b) M L T− −1 1 c) 1−MLT d) M L T2 2 1− −

34. If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, then non-z e r o i n t e g e r s x, y and z, such that Px Qy cz is dimensionless, area) x = 1, y = 1, z = -1 b) x = 1, y = -1, z = 1 c) x = -1, y = 1, z = 1 d) x = 1, y = 1, z = 1

35. If x = ( a/b ), the maximum percentage error in the measurement of x will be

a) ∆ ∆aa

bb

×FHGIKJ ×FHG

IKJ100% 100%/ b)

∆ ∆aa

bb

×FHGIKJ × ×FHG

IKJ100% 100%

c)∆ ∆aa

bb

+FHGIKJ ×100% d)

∆ ∆aa

bb

−FHGIKJ ×100%

36. While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of thependulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation

)T/(4g 22π= will be

a) 2% b) 4% c) 7% d) 10%

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37. If x = a - b, the maximum percentage error in the measurement of x will be

a)∆ ∆aa

bb

+FHGIKJ ×100% b)

∆ ∆aa

bb

−FHGIKJ ×100%

c)∆ ∆aa b

ba b−

+−

FHG

IKJ ×100% d)

∆ ∆aa b

ba b−

−−

FHG

IKJ ×100%

38. The volume of one sphere is 1.76 cc. The volume of 25 such spheres ( according to the idea of significant figure ) is

a) 44.00 cc b) 44.0 cc c) 44 cc d) 0.44 × 102 cc

39. Which one of the following has not been expressed in proper unitsa) { Stress / Strain } = N/m2 b) Surface Tension = N/m c) Energy = kg × m/sec d) Pressure = N/m2

40. Let A = i A cos θ + j A sin θ be any vector. Another vector B, which is normal to A can be expressed as

a) i B cos θ - j B sin θ b) i B cos θ + j B sin θ c) i B sin θ - j B cos θ d) i B sin θ + j B cos θ

41. Angular momentum isa) scalar b) a polar vector c) an axial vector d) linear momentum

42. A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10metres per minute in still water, wants to swim across the river in shortest time. He should swim in a direction :a) due north b) 30° east of north c) 30° west of north d) 60° east of north

43. A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocityof the river water in km/hr is

a) 1 b) 3 c) 4 d) 41

44. Out of the following sets of forces, the resultant of which cannot be zero

a) 10, 10, 10 b) 10, 10, 20 c) 10, 20, 20 d) 10, 20, 40

45. Three vectors A, B and C satisfy the relation 0=• BA and 0=•CA . The vector A is parallel to

a) B b) C c) CB • d) CB×

46. The vectors A and B are such that |||| BABA −=+ then the angle between the two vectors will be

a) 0° b) 60° c) 90° d) 180°

47. A truck travelling due North at 20 m/sec turns West and travels at the same speed. Then the change in velocity is

a) 40 m/sec North West b) 20 2 m/sec North West c) 40 m/sec South West d) 20 2 m/sec South West

48. A point of application of a force F = 5i - 3j + 2k is moved from r1 = 2i + 7j + 4k to r2 = -5i + 2j + 3k. The work done is

a) -22 units b) 22 units c) 11 units d) 0 units.

49. The vector sum of n coplanar forces, each of magnitude F, when each force is making an angle of n/2π with the proceeding one, isa) zero b) nF c) F/2 d) nF/2

50. A boat is moving with a velocity 3i + 4j with respect to ground. The water in the river is moving with a velocity - 3i - 4j with respect to ground.The relative velocity of the boat with respect to water isa) 8j b) -6i - 8j c) 6i + 8j (d) 25

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Answers

1. b 2. d 3. c 4. c 5. c 6. c7. a 8. a 9. a 10. c 11. b 12. c13. a 14. a 15. a 16. a 17. a, d 18. a, b,c19. c 20. a 21. d 22. d 23. a 24. c25. b 26. d 27. d 28. a 29. b 30. b31. c 32. a 33. b 34. b 35. c 36. c37. c 38. b 39. c 40. c 41. c 42. c43. b 44. d 45. d 46. c 47. d 48. a49. a 50. c

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WAVE MOTION

1. An astronaut can't hear his companion at the surface of the moon becausea) produced frequencies are above the radio frequenciesb) there is no medium for sound propagationc) temperature is too low during night and too high during dayd) there are too many craters on the surface of the moon.

2. Which of the following expressions is that of a simple harmonic progressive wavea) tsina ω b) )kxcos()t(sina ω c) )kxt(sina −ω d) kxcosa .

3. The displacement represented by y x t a kx t( , ) cos( )= +ω representsa) transverse wave propagating in +x direction b) transverse wave propagating in -x directionc) longitudinal wave propagating in +x direction d) longitudinal wave propagating in - x direction

4. A transverse wave is described by the equation Y = Y0 sin 2 π (ft - λπ / ). The maximum particle velocity is equal to four times the wave

velocity if °y is equal to

a) λf b) πλ /2 c) λf2 d) πλ /

5. The equation of a wave travelling in a string can be written as y = 3 cos π ( 100 t - x ). Its wavelength isa) 100 cm b) 2 cm c) 5 cm d) none of these

6. The equation of a transverse wave is given by y x t= −10 0 01 2sin ( . )π where y and x are in cm and t is in sec. Its frequency isa) 10 sec-1 b) 2 sec-1 c) 1 sec-1 d) 0.01 sec-1

7. The diagram shows the propagation of a wave. Which points are in phase

a) A and B b) B and C

c) B and D d) E and B

8. The sound carried by air from a sitar to a listener is a wave of the following typea) longitudinal stationary b) transverse progressive c) transverse stationary d) longitudinal progressive

9. Sound waves are travelling in a medium whose adiabatic elasticity is E and isothermal elasticity E'. The velocity of sound wave is proportionalto

a) E' b) E c) E ' d) E/E'

10. The temperature at which the speed of sound in air becomes double of its value at 27°C isa) 54°C b) 327°C c) 927°C d) -123°C

11. Velocity of sound is measured in hydrogen and oxygen gases at a given temperature. The ratio of two velocities will be (VH / V0 )a) 1 : 4 b) 4 : 1 c) 1 : 1 d) 32 : 1

12. If the amplitude of waves at a distance r from a line source is A, then the amplitude at a distance 4r will bea) 2A b) A c) A/2 d) A/4

13. A particle is oscillating according to the equation x = 7 cos 0.5 π t, where t is in seconds. The point moves from the position of equilibriumto maximum displacement in timea) 4.0 s b) 2.0 s c) 1.0 s d) 0.5 s

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14. The amplitude of a damped oscillator becomes half in 1 minute. The amplitude after 3 minutes will be 1/x times the original, where x isa) 2 × 3 b) 23 c) 3 2 d) 3 × 22

15. The distance between two points differing in phase by 60° on a wave having a wave velocity 360 metre/sec and frequency 500 Hz isa) 0.72 meter b) 0.18 meter c) 0.12 meter d) 0.36 meter

16. When a sound wave of frequency 300 Hz passes through a medium, the maximum displacement of a particle of the medium is 0.1 cm. Themaximum velocity of the particle is equal toa) 60 π cm/s b) 30 π cm/s c) 30 cm/s d) 60 cm/s

17. Two particles P and Q describe S.H.M. of same amplitude a, frequency v along the same straight line. The maximum distance between the

two particles is a 2. The initial phase difference between the particle isa) zero b) π /2 c) π /6 d) π /3

18. A sound wave travelling with a velocity v in a medium A reaches a point on the interface of medium A and medium B. If the velocity in themedium B be 2v, the angle of incidence for total internal reflection of the wave will bea) > 15° b) > 30° c) > 45° d) > 90°

19. The complete destructive interference of two sound waves takes place when the two waves are travelling in the same directiona) with the same frequency and amplitude and are in phase b) with the same frequency and amplitude and are in opposite phasec) with the same frequency and amplitude d) with the same frequency and opposite phase.

20. If the intensities of the interfering waves be I1 and I2, then the contrast between maximum and minimum intensity is good whena) I1 >> I2 b) I1 << I2 c) I1 = I2 d) either I1 or I2 is zero.

21. Two adjacent piano keys are struck simultaneously. The notes emitted by them have frequencies n1 and n2. The number of beats heard persecond isa) ( ) /n n1 2 2− b) ( ) /n n1 2 2+ c) n n1 2− d) 2 1 2( )n n−

22. If two tuning forks A and B are sounded together, they produce 4 beats per second. A is then slightly loaded with wax, they produce twobeats when sounded again. The frequency of A is 256. The frequency of B will bea) 250 b) 252 c) 260 d) 262

23. Two tuning forks of frequencies 256 and 258 vibrations / second are sounded together. Then the time interval between two consecutivemaxima heard by an observer isa) 2 second b) 0.5 second c) 250 second d) 252 second

24. Tuning fork A of frequency 258 cycles / sec gives 8 beats with a tuning fork B. When prongs of B are cut and again A and B are sounded,the number of beats heard remains same. The frequency of B in cycles / sec isa) 250 b) 264 c) 242 d) 258

25. 41 tuning forks are arranged so that every fork gives 5 beats with the next. The last fork has frequency that is double of the first. Thefrequency of first fork isa) 200 b) 400 c) 205 d) 210

26. Beats are produced by two progressive waves of equal amplitudes. Maximum loudness at the waxing is x times the loudness of each wave.The value of x is

a) 1 b) 2 c) 2 d) 4

27. Two sounding bodies producing progressive waves given by y t1 4 400= sin π and y t2 3 404= sin π are situatedvery near to the ears of a person who will hear

a) 2 beats per second with intensity ratio ( 4/3 ) between maxima and minima

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b) 2 beats per second with intensity ratio ( 49/1 ) between maxima and minimac) 4 beats per second with intensity ratio ( 7/1 ) between maxima and minimad) 4 beats per second with intensity ratio ( 4/3 ) between maxima and minima

28. Stationary waves are formed whena) two waves of equal amplitude and equal frequency travel along the same path in opposite directionsb) two waves of equal wavelengths and amplitude travel along the same path with equal speeds in opposite directionsc) two waves of equal wavelengths and equal phase travel along the same path with same speedd) two waves of equal amplitude and speed travel along the same path in opposite directions.

29. The equation of stationary wave is given bya) y y kx t= 2 0 sin cosω b) y y k x vt= −0 sin ( )

c) y y k x tT

= −FHGIKJ0 2cos π

λ d) y y v T= 0

2sinλ

30. Phase difference between two particles of a medium lying between two consecutive nodes isa) zero b) π /4 c) π /2 d) π

31. The equation of stationary wave is given by y x t= 5 3 40cos( / ) sinπ π where y and x are given in centimeters and time t inseconds, then the amplitude of the progressive wave isa) 5 cm b) 2.5 cm c) 10 cm d) 3 cm

32. For the stationary wave y x t= 4 15 96sin( / ) cos( )π π the distance between a node and the next antinode isa) 7.5 b) 15 c) 22.5 d) 30

33. Two loudspeakers L1 and L2 driven by a common oscillator and amplifier are set up as shown in the figure. As the frequency of the oscillatorincreases from zero, the detector at D recorded a series of maximum and minimum signals.What is the frequency at which the first maximum is observed ? ( Speed of sound = 330 m/s ).

a) 165 Hz b) 330 Hz c) 495 Hzd) 660 Hz

34. A sonometer wire of density d and radius a is held between two bridges at a distance L apart. The wire has a tension T. The fundamentalfrequency of the wire will be

a) n laT d

=FHGIKJ

12

2πb) n l

Ta d

=FHGIKJ

12 2π c) n

lT da

=FHGIKJ

12 2π d) n

lT a d=

12

2( )π

35. In a long cylindrical tube, the water level is adjusted and the air column above it is made to vibrate in unison with a vibrating tuning fork keptat the open end. Maximum sound is heard when the air column lengths are equal to

(a)λ λ λ4 2

34

, , (b)λ

λλ

232

, , c)λ λ λ23252

, , d)λ λ λ43454

, ,

36. There are two open organ pipes of exactly the same length and material but different radii. Thena) wider pipe has lower frequency b) narrower pipe has lower frequencyc) both the pipes have same frequency d) It cannot be said based on given data

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37. A cylindrical tube, open at both ends, has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it is in water. Thefundamental frequency of the air column is nowa) f / 2 b) 3f / 4 c) f d) 2f.

38. Transverse waves are generated in two uniform wires A and B of same material by attaching their free ends to a vibrating source offrequency 200 Hz. The cross sectional area A is half that of B while the tension on A is twice that on B. The ratio of the wavelengths of thetransverse waves in A and B isa) 1 : 2 b) 2 : 1 c) 1 : 2 d) 2 : 1

39. A stretched string of 1 m length, fixed at both ends, having a mass of 5 × 10-4 kg is under a tension of 20 N. It is plucked at a point situatedat 25 cm from one end. The stretched string would vibrate with a frequency ofa) 400 Hz b) 100 Hz c) 200 Hz d) 256 Hz

40. A wire under tension vibrates with a fundamental frequency of 450 per second. What would be the fundamental frequency if the wire werehalf as long, having twice the diameter and under one fourth tension.a) 225 cps b) 190 cps c) 247 cps d) 174 cps

Answers

1. b 2. c 3. b 4. b 5. b 6. c7. d 8. d 9. b 10. c 11. b 12. c13. c 14. b 15. c 16. a 17. b 18. b19. b 20. c 21. c 22. b 23. b 24. a25. a 26. d 27. b 28. b 29. a 30. d31. b 32. a 33. b 34. b 35. d 36. c37. c 38. d 39. c 40. a

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WAVE OPTICS

1. In figure, a wave front AB moving in air is incident on a plane glass surface XY. Its position CD after refraction through a glass slab is shownalso along with the normal drawn at A and D. The refractive index of the glass with respect to air will be equal to

θ

θφ

φ

D

B

C

AX Y

AIR

GLASS

O

a) BD/AC b) AB/CD c) BD/AD d) AC/AD

2. Laser light is considered to be coherent because it consists ofa) may wavelength b) uncoordinated wavelengthc) coordinated waves of exactly the same wavelength d) divergent beam

3. In the Young's double slit experiment, the interference pattern is found to have an intensity ratio between bright and dark fringes, as 9. Thisimplies thata) the intensities at the screen due to the two slits are 5 units and 4 units respectively.b) the intensities at the screen due to the two slits are 4 units and 1 unit respectively.c) the amplitude ratio is 3.d) the amplitude ratio is 2.

4. In Young's double slit experiment, the separation between the slit is halved and the distance between the slits and screen is doubled. Thefringe width isa) unchanged b) halved c) double d) quadrupled

5. In Young's experiment, the wavelength of red light is 7.8 × 10-5 cm and that of blue light 5.2 × 10-5 cm. The value of n for which ( n + 1 )th bluebright band coincides with nth red band isa) 4 b) 3 c) 2 d) 1

6. We shift Young's double slit experiment from air to water. Assuming that water is still and clear, it can be predicted that the fringe pattern willa) remain unchanged b) disappear c) shrink d) be enlarged

7. In Young's double slit interference experiment, the distance between two sources is 0.1 mm. The distance of the screen from the sourcesis 20 cm. Wavelength of light used is 5460 Å. Then the angular position of the first dark fringe isa) 0.08° b) 0.16° c) 0.20° d) 0.32°

8. If one of the two slits of a Young's double slit experiment is painted over so that it transmits half the light intensity of the other thena) the fringe system would disappearb) the bright fringes will be more bright and dark fringes will be more darkc) the dark fringes would be bright and bright fringes would be darkerd) bright as well as dark fringes would be darker

9. In Young's double slit experiment, if two slightly different wavelengths are present in the light used, thena) the sharpness of fringes will increase every where ( compared to the case when monochromatic light is used )b) there will be no fringes at allc) the sharpness of fringes will decrease as we move away from central fringe.d) the central fringe will be white.

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10. In Young's double slit experiment, illuminated by yellow light, one slit is covered with plane transparent thin glass plate and the other slit by bluefilter. Thena) there will be yellow and blue interference fringes formed on the screen.b) there will be uniform illumination on the screen.c) the maximum intensity fringes will be double coloured.d) the minimum intensity fringes will be dark.

11. In the Young's double slit experiment, the two equally bright slits are coherent, but of phase difference p/3. If the maximum intensity on thescreen is I0, the intensity at the point on the screen equidistant from the slits isa) I0 b) I0/2 c) I0/4 d) 3I0/4

12. In an interference pattern produced by two identical slits, the intensity at the site of the central maximum is I. The intensity at the same spotwhen either of the two slits is closed is I0. thereforea) I = I0 b) I = 2I0 c) I = 4I0 d) I = I0 are not related to each other

13. In a Young's double slits experiment, the source S and two slits A and B are horizontal, with slit A above slit B. The fringes are observed ona vertical screen K. The optical path length from S to B is increased very slightly ( by introducing a transparent material of higher refractiveindex ( and optical path length from S to A is not changed. As a result the fringe system on K movesa) vertically downwards slightly b) vertically upwards slightlyc) horizontally, slightly to the left d) horizontally, slightly to the right

14. Two waves originating from source S1 and S2 having zero phase difference and common wavelength l will show completely destructiveinterference at a point P if ( S1 P - S2 P ) isa) 5λ b) 3λ / 4 c) 2λ d) 11λ / 2

15. When light wave suffers reflection at the interface between air and glass, the change of phase of the reflected wave is equal toa) zero b) π /2 c) π d) 2π

16. Four independent waves are expressed as y1 = a1 sin ω t, y2 = a2 sin 2ω t, y3 = a3 cos ω t and y4 = a4 sin (ω t + π /3 ). The interferenceis possible betweena) (i) and (iii) b) (i) and (iv) c) (iii) and (iv) d) all of the above

17. In a two slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen ismoved by 5 × 10-2 m towards the slits, the change in fringe width is 3 × 10-5 m. If separation between the slits is 10-3 m, the wavelength oflight used isa) 6000 Å b) 5000 Å c) 3000 Å d) 4500 Å

18. Light travels faster in air than in glass according toa) Wave theory of light b) Corpuscular theory of light c) Both 1 and 2 d) Neither 1 or 2

19. The condition for observing Fraunhofer diffraction from a single slit is that the light wavefront incident on the slit should bea) spherical b) cylindrical c) plane d) elliptical

20. The first diffraction minima due to a single slit diffraction is at θ = 30° for a light of wavelength 5000 Å. The width of the slit isa) 5 × 10-4 cm b) 1.0 × 10-4 cm c) 2.5 × 10-4 cm d) 1.25 × 10-4 cm.

21. To observe diffraction, the size of an obstaclea) should be of the same order as wavelength b) should be much larger than the wavelengthc) have no relation to wavelength d) should be exactly λ /2

22. A diffraction pattern is obtained using a beam of red light. What happens if the red light is replaced by blue lighta) no change b) diffraction bands become narrower and crowded togetherc) bands become broader and farther apart d) bands disappear

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23. Light of wavelength 6328 Å is incident normally on a slit having a width of 0.2 mm. The width of the central maximum measured from minimum tominimum of diffraction pattern on a screen 9.0 metres away will be about

a) 0.36 degrees b) 0.18 degrees c) 0.72 degrees d) 0.09 degrees

24. The transverse nature of light is shown by

a) interference of light b) refraction of light c) polarisation of light d) dispersion of light

25. When unpolarised light is incident on a plane glass plate at Brewster's ( polarising ) angle, then which of the following statements is correcta) reflected and refracted rays are completely polarised with their planes of polarisation parallel to each other.b) reflected and refracted rays are completely polarised with their planes of polarisation perpendicular to each other.c) the reflected light is plane polarised but transmitted light is partially polarised.d) the reflected light is partially polarised but refracted light is plane polarised.

26. In a biprism experiment using sodium light of Å60001 =λ , an interference pattern is obtained in which 20 fringes occupy 2.0 cm. On

replacing the sodium source by a source of wavelength 2λ , while making no other changes, 30 fringes are found to occupy 2.7 cm on the

screen; 2λ isa) 4500 Å b) 5400 Å c) 5600 Å d) 4200 Å

27. A glass slab of thickness 4 cm contains the same number of waves as 5 cm of water when both are transversed by the same monochromaticlight. If the refractive index of water is 4/3, what is the refractive index of glass ?a) 5/3 b) 5/4 c) 16/15 d) 3/2

28. The colour of thin films results froma) dispersion b) interference c) absorption d) scattering

29. Light appears to travel in a straight line becausea) it emits small particles b) the velocity of light is very largec) the wavelength of light is very small d) light is reflected by the surroundings

Answers

1. a 2. c 3. b, d 4. d 5. c 6. c7. b 8. c 9. c 10. b 11. d 12. c13. a 14. d 15. c 16. d 17. a 18. a19. c 20. b 21. a 22. b 23. b 24. c25. c 26. b 27. a 28. b 29. c

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