Topper’s Package Physics - XI Conservation of Momentum ......2020/07/21 · Topper’s Package Physics - XI Conservation of Momentum and Centre of MassPermutation and Combinations

Topper’s Package Physics - XI Permutation and CombinationsConservation of Momentum and Centre of Mass

58

1. CONSERVATION OF MOMENTUM

1. On a smooth horizontal surface, a ring of massM lies with two insects of mass m, on itsdiametrically opposite points. The insectsmove with velocity v along the ring. The velocityof the ring as the insects meet is

(a)m

Mv2

(b)mMmM

(c) zero (d) vMm2

2. A particle of mass m is made to move withuniform speed 0v along the perimeter of aregular hexagon. The magnitude of impulseapplied at each corner of the hexagon is

(a) 02mv sin6

(b) 0mv sin6

(c) 0mv sin3

(d) 02mv sin3

3. A stationary radioactive nucleus of mass 210units disintegrates into an -particle of mass4 units and a residual nucleus of mass 206units. If the kinetic energy of -particle is E,the kinetic energy of residual nucleus will be

(a)E

206 (b)2E

103

(c)E

412 (d)E

1034. A shell is fired from a cannon with velocity v

m/s at an angle with the horizontaldirection. At the highest point in its path, itexplodes into two pieces of equal mass. One ofthe pieces retraces its path to the cannon. Thespeed of other piece immediately afterexplosion is

(a) 3 cosv (b) 3 cos2

g

(c) 2 cosv (d)3 cos2

v

5. A bomb of mass 9 kg explodes into two piecesof mass 3 kg and 6 kg. The velocity of the massof 3 kg is 16 m/sec. The kinetic energy ofmass 6 kg is(a) 96 J (b) 192 J(c) 384 J (d) 768 J

6. A bead can slide on a smooth straight wire anda particle of mass m is attached to the bead bya light string of length L. The particle is heldin contact with the wire with the string tautand is then let fall. If the bead has mass 2 m .Then, when the string makes an angle withthe wire the bead will have slipped a distance

L

2m

(a) (1 cos )L (b) (1 cos )2L

(c) (1 cos )3L

(d) (1 cos )6L

7. A block of mass m is pushed towards a movablewedge of mass 2 m and height h with a velocityu. All surfaces are smooth. The minimum valueof u for which the block will reach the top ofthe wedge is

2mm

h

u

(a) 2 gh (b) 3gh

(c) 6gh (d)32

gh

8. An isolated particle of mass m is moving inhorizontal plane (x-y), along the x-axis, at acertain height above the ground. It suddenly

explodes into two fragments of masses 4m

and34m

. An instant later, the smaller fragment is

at 15y cm . The larger fragment at this

Conservation of Momentumand Centre of Mass

Unit 5

Topper’s Package Physics - XI Physical World & MeasurementPermutation and CombinationsConservation of Momentum and Centre of Mass

59

instant is at(a) 5 cmy (b) 20 cmy(c) 5 cmy (d) 20 cmy

9. A boy of mass 60 kg is standing over a platformof mass 40 kg placed over a smooth horizontalsurface. He throws a stone of mass 1 kg withvelocity 10 /u m s at an angle of 45° withrespect to ground. The displacement of platform(with boy) on the horizontal surface, when thestone lands on the ground is 2( 10 / )g m s(a) 25 cm (b) 5 cm(c) 10 cm (d) 50 cm

10. A mass 2 m rests on a horizontal table. It isattached to a light inextensible string whichpasses over a smooth pulley and carries a massm at the other end. If the mass m is raisedvertically through a distance h and is thendropped, then the speed with which the mass2 m begins to rise is

(a) 2gh

(b)23gh

2m

m

m

h(c)

2gh

(d) gh

11. A balloon has 2g of air. A small hole is piercedinto it. The air comes out with relative velocity4 m/s. If the balloon shrinks completely in 2.5s,the average force acting on the balloon is(a) 0.008 N (b) 0.0032 N(c) 8 N (d) 3.2 N

2. COLLISSION12. A bullet in motion hits and gets embedded in a

solid block resting on a frictionless table. Whatis conserved for the bullet-block system?(a) Momentum and KE(b) Kinetic energy alone(c) Neither KE nor momentum(d) Momentum alone

13. Two identical billiard balls are in contact on atable. A third identical ball strikes themsymmetrically and remains at rest after impact.The coefficient of restitution is

(a)32

(b)31

(c)61

(d)23

14. A small spherical ball strikes a frictionlesshorizontal plane with a velocity v making anangle to the normal at the surface. If thecoefficient of restitution is e, the particle willagain strike the surface after time

(a)2vsin

g

(b)2evcos

g

(c)2evsin

g

(d)2v cos

g

15. A smooth ball of mass m strikes a horizontalsurface with a velocity v in a direction makingan angle 30° with the normal to the surface asshown in the figure. If the coefficient ofrestitution for the collision between the balland the surface is e and the ball was in contactwith the surface for a small time ‘ t ’ theaverage force acting on the ball duringcollision is

v30°

(a) mg (b)mv(1 e)

2 t

(c)3mv(1 e)

2 t

(d)

3mv(1 e)2 t

16. Four particles A, B, C and D of equal mass movewith equal speed v along the diagonals of asquare in a horizontal plane as shown in thefigure. After the collision A comes to rest, Band C retrace their paths. Then the particle Dwill

A B

C D(a) Continue to move along the same line with

speed v(b) Retrace its path with speed 2v(c) Comes to rest(d) Move with speed 2v along a line parallel

to CD


60

17. A bag of sand of mass M is suspended by a rope.A bullet of mass M/20 is fired at it with avelocity v and get embedded into it. The velocityof bag just after bullet gets embedded is

(a)v

20 × 21 (b)2021

v

(c)v

20 (d)v21

18. A ball falls vertically onto a floor, withmomentum p, and then bounces repeatedly,the coefficient of restitution is e. The totalmomentum imparted by the ball to the floor is

(a) p (1 + e) (b)p

e1

(c) p 11

FHG

IKJ

ee

(d) p 1 1F

HGIKJe

19. A particle strikes a horizontal frictionless floorwith a speed u at an angle with the vertical,and rebounds with a speed v at an angle with vertical. The coefficient of restitutionbetween the particle and floor is e. Themagnitude of v is(a) eu(b) (1 – e) u

(c) 2 2 2u e sin cos

v u

N

O (d) 2 2 2u sin e cos

20. A mass m moving horizontally with velocity 0vstrikes a pendulum of mass m. If the twomasses stick together after the collision, thenthe maximum height reached by thependulum is(a) 0v g (b) 02v g

(c)20

2v

g (d)20

8v

g

21. A ball is dropped from a height h on the ground.If the coefficient of restitution is e, the heightto which the ball goes up after it rebounds forthe nth time is(a) 2nhe (b) nhe(c) 2 /ne h (d) 2/ nh e

22. A ball of mass m moving at a speed v makes ahead on collision with identical ball at rest.The kinetic energy of the balls after collision

is 34

th of the original. The coefficient ofrestitution is

(a)12 (b)

12

(c)34

(d)32

23. A sphere of mass m moving with a constantvelocity u hits another stationary sphere of thesame mass. If e is the coefficient of restitution,then the ratio of the velocity of the two spheresafter collision will be

(a)11

ee

(b)11

ee

(c)11

ee

(d)21

1e te

24. A mass m moves with a velocity v and collides

inelastically with another identical mass. After

collision the first mass moves with velocity 3v

in a direction perpendicular to the initialdirection of motion. The speed of the 2nd massafter collision

m

v

mat rest before collision

after collision

v3

(a)23

v (b) 3v

(c) v (d) 3v

25. After perfectly inelastic collision between twoidentical particles moving with same speed indifferent direction, the speed of the particlesbecome half the initial speed. The anglebetween the velocities of the two beforecollision is(a) 60° (b) 45°(c) 120° (d) 30°

26. A projectile of mass 3m explodes at highestpoint of its path. It breaks into three equal parts.One part retraces its path, the second onecomes to rest. The range of the projectile was100m if no explosion would have taken place.The distance of the third part from the point ofprojection when it finally lands on the groundis


61

(a) 100 m (b) 150m(c) 250m (d) 300m

27. In a one dimensional collision between twoidentical particles A and B, B is stationary andA has momentum P before impact. Duringimpact B gives an impulse J to A. Thencoefficient of restitution between the two is

(a)2 1JP

(b)2 1JP

(c) 1JP (d) 1J

P

28. Two identical balls A and B are released fromthe positions shown in figure. They collideelastically on horizontal portion MN. The ratioof heights attained by A and B after collisionwill be : (Neglect friction)

45° 60°

M

4h

N

A

B

h

(a) 1 : 4 (b) 2 : 1(c) 4 : 13 (d) 2 : 5

29. A smooth sphere is moving on a horizontalsurface with velocity vector ˆ ˆ2 2i jimmediately before it hits a vertical wall. Thewall is parallel to j vector and the coefficientof restitution between the sphere and the wallis 1/2. Find the velocity of sphere after it hitsthe wall(a) ˆ ˆi j (b) ˆ ˆ2i j (c) ˆ ˆi j (d) ˆ ˆ2i j

30. A particle of mass m moving in the x directionwith speed 2v is hit by another particle of mass2m moving in the y direction with speed v. Ifthe collision is perfectly inelastic, thepercentage loss in the energy during thecollision is closse to :(a) 56 % (b) 62%(c) 44% (d) 50%

31. Two solid rubber balls A and B having masses200 and 400g respectively are moving inopposite directions with velocity of A equal to0.3 m/s. After collision the two balls come torest, then the velocity of B is

(a) 0.15 m/sec (b) 1.5 m/sec(c) –0.15 m/sec (d) None of the above

32. Two identical ball bearings in contact witheach other and resting on a frictionless tableare hit head-on by another ball bearing of thesame mass moving initially with a speed Vas shown in figure

If the collision is elastic, which of thefollowing (figure) is a possible result aftercollision

(a) (b)

(c) (d)

33. Two balls at same temperature collide. Whatis conserved(a) Temperature (b) Velocity(c) Kinetic energy (d) Momentum

34. Two equal masses m1 and m2 moving alongthe same straight line with velocities +3 m/s and –5 m/s respectively collide elastically.Their velocities after the collision will berespectively(a) +4 m/s for both(b) –3 m/s and +5 m/s(c) –4 m/s and +4 m/s(d) –5 m/s and +3 m/s

35. A ball of mass m falls vertically to the groundfrom a height h1 and rebound to a height h2.The change in momentum of the ball onstriking the ground is(a) 1 2( )mg h h (b) 1 2( 2 2 )m gh gh(c) 1 22 ( )m g h h (d) 1 22 ( )m g h h

36. A big ball of mass M, moving with velocity ustrikes a small ball of mass m, which is atrest. Finally small ball obtains velocity u andbig ball v. Then what is the value of v

(a) M m uM (b) m u

M m(c) 2m u

M m (d) M uM m


62

37. A mass of 100g strikes the wall with speed5m/s at an angle as shown in figure and itrebounds with the same speed. If the contacttime is 2 10–3 sec, what is the force applieson the mass of the wall

(a) 250 3 N to right (b) 250 N to right(c) 250 3 N to left (d) 250 N to left

38. A spherical ball A of mass 4kg, moving alonga straight line strikes another spherical ballB of mass 1kg at rest. After the collision. Aand B move with velocities v1 ms–1 and v2ms–1 respectively making angles of 30° and60° with respect to the original direction ofmotion of A. The ratio 1

2

vv will be

(a) 3 /4 (b) 4 / 3(c) 1/ 3 (d) 3

39. A billiards player hits a stationary ball by anindentical ball to pocket the target ball in acorner pocket that is at an angle of 35° withrespect to the direction of motion of the firstball. Assuming the collision as elastic and thatfriction and rotational motion are notimportant, the angle made by the target ballwith respect to the incoming ball is(a) 35° (b) 50°(c) 55° (d) 60°

40. Three objects A, B and C are kept in a straightline on a frictionless horizontal surface.Thesehave masses m, 2m and m, respectively. Theobject A moves towards B with a speed 9m/s and makes an elastic collision with it.Thereafter, B makes completely inelasticcollision with C. All motions occur on thesame straight line. Find the final speed (inm/s) of the object C

m m2mA B C

(a) 3m/s (b) 4m/s(c) 5m/s (d) 1m/s

41. A sphere of mass m moving with a constantvelocity u hits another stationary sphere ofthe same mass. If e is the coefficient ofrestitution, then the ratio of the velocity oftwo spheres after collision will be

(a) 11

ee

(b) 1

1ee

(c) 11

ee (d) 21

1e te

42. A ball of mass 0.2 kg rests on a vertical postof height 5 m. A bullet of mass 0.01 kg,traveling with a velocity V m/s in a horizontaldirection, hits the centre of the ball. After thecollision, the ball and bullet travelindependently. The ball hits the ground at adistance of 20 m and the bullet at a distanceof 100 m from the foot of the post. The initialvelocity V of the bullet is

(a) 250 m/s (b) 250 2 /m s(c) 400 m/s (d) 500 m/s

43. A ball is allowed to fall from a height of 10m.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

44. A body of mass m1 moving with velocity3 ms–1 collides with another body at rest ofmass m2. After collision the velocities of thetwo bodies are 2 ms–1 and 5 ms–1 respectivelyalong the direction of motion of m1. The ratiom1/m2 is

(a) 512 (b) 5

(c) 15 (d) 12

5

45. Two partilces of masses m1, m2 move withinitial velocities u1 and u2. On collision, oneof the particles get excited to higher level,after absorbing energy if final velocities of


63

partcles be v1 and v2 then must have

(a) 2 2 2 21 1 2 2 1 1 2 2

1 1 1 12 2 2 2

m u m u m v m v

(b) 2 2 2 21 1 2 2 1 1 2 2

1 1 1 12 2 2 2

m u m u m v m v

(c) 2 2 2 21 1 2 2 1 1 2 2

1 1 1 12 2 2 2

m u m u m v m v

(d) 2 2 2 21 1 2 2 1 1 2 2

1 12 2

m u m u m v m v

46. A particle falls from a height h upon a fixedhorizontal plane and rebounds. If e is thecoefficient of restitution, the total distancetravelled before rebounding has stopped is

(a)2

211

ehe

(b)

2

211

ehe

(c)2

21

2 1h e

e

(d)

2

21

2 1h e

e

47. Two small particles of equal masses startmoving in opposite directions from a point Ain a horizontal circular orbit. Their tangentialvelocities are v and 2v, respectively, as shownin the figure. Between collisions, the particlesmove with constant speeds. After making howmany elastic collisions, other than that at A,these two particles will again reach the pointA

AV 2V

(a) 4 (b) 3(c) 2 (d) 1

48. A ball is droped vertically from a height of honto a hard surface. If rebounds from thesurface with a fraction r of the speed withwhich it strikes the latter on each impact,what is the net distance travelled by the ballup to the 10th impact

(a)1012

1rhr

(b)20

211

rhr

(c)22

2121

rh hr

(d)20

2121

rh hr

49. A narrow but tall cabin is falling freely nearthe earth’s surface. Inside the cabin, twosmall stones A and B are released from rest(relative to the cabin). Initially A is muchabove the centre of mass and B much belowthe center of mass of cabin. A close observationof the motion of A and B will reveal that(a) Both A and B continue to be exactly at rest

relative to the cabin(b) A moves slowly upward and B moves slowly

downward relative to the cabin(c) Both A and B fall to the bottom of the cabin

with constant acceleration due to gravity(d) A and B move slightly towards each other

vertically

50. An electron collides with a free moleculesinitially in its ground state. The collisionleaves the molecules in an excited state thatis meta stable and does not decay to theground state by radiation. Let K be the sumof the initial kinetic energies of the electronand the molecule, and P

the sum of their

initial momenta. Let K and P represent the

same physical quantities after the collision.Then(a) ,K K P P

(b) ,K K P P

(c) ,K K P P

(d) ,K K P P

51. A ball of mass m suspended from a rigidsupport by an inextensible massless string isreleased from a height h above its lowest point.At its lowest point it collides elastically witha block of mass 2m at rest on a frictionlesssurface. Neglect the dimensions of the balland the block. After the collision the ball risesto a maximum height of

(a) 3h (b) 2

h

(c) 8h (d) 9

h


64

52. A small boy is throwing a ball towards a wall6m in front of him. He releases the ball ata height of 1.4m from the ground. The ballbounces from the wall at a height of 3mrebounds from the ground and reaches theboy’s hand exactly at the point of release.Assuming the two bounces (one from the walland the other from the ground) to be perfectlyelastic, how far ahead of the boy did the ballbounce from the ground(a) 1.5 m (b) 2.5 m(c) 3.5 m (d) 4.5 m

53. A particle A of mass m and initial velocity v

collides with a particle B of mass 2m which

is at rest. The collision is head on, andelastic. The ratio of the de-Brogliewavelengths A to B after the collision is

(a)12

A

B

(b)13

A

B

(c) 2A

B

(d)23

A

B

54. A moving block having mass m, collides with

another stationary block having mass 4 m.The lighter block comes to rest after collision.When the initial velocity of the lighter blockis v, then the value of coefficient of restitution(e) will be(a) 0.5 (b) 0.25(c) 0.8 (d) 0.4

55. It is found that if a neutron suffers an elasticcollinear collision with deuterium at rest,fractional loss of its energy is Pd, while forits similar collision with carbon nucleus atrest, fractional loss of energy is pc. The valuesof pd and pc are respectively :(a) (0, 0) (b) (0, 1)(c) (.89, .28) (d) (.28, .89)

56. Quantity/Quantities remaining constant ina collision is/are(a) Momentum, kinetic energy and

temperature(b) Momentum but not kinetic energy and

temperature(c) Kinetic energy and temperature but not

momentum(d) None of the above

57. A body falls on a surface of coefficient ofrestitution 0.6 from a height of 1 m. Thenthe body rebounds to a height of(a) 0.6 m (b) 0.4 m(c) 1 m (d) 0.36 m

58. Which of the following is true for any collision(a) Both linear momentum and kinetic

energy are conserved(b) Neither linear momentum nor kinetic

energy may be conserved(c) Linear momentum is always conserved,

however, kinetic energy may or may notbe conserved

(d) Kinetic energy is always conserved, butlinear momentum may or may not beconserved

3. CENTER OF MASS

59. Consider a system of two identical particles.One of the particles is at rest and other hasacceleration a . The centre of mass hasacceleration

(a) Zero (b) a21

(c) a (d) a2

60. A chain of mass M is placed on a smoothtable with 1/n of its length L hanging overthe edge. The work done in pulling the hangingportion of the chain back to the surface ofthe table is

(a)MgL

n (b) 2MgL

n

(c) 2MgLn

(d) 22MgL

n61. A man of mass m stands at one end of a wooden

plank of mass M and length L. The plank isfloating in water. The man walks from one endof the plank to the other and stops. Thedisplacement of the plank is

(a) ( )Lm

M m (b) ( )LM

M m

(c) ( )m M mL

(d) ( )M M mL

62. A uniform rod of length l is kept vertically on arough horizontal surface at 0x . It is rotatedslightly and released. When the rod finally fallson the horizontal surface, the lower and willremain at


65

x = 0x-axis

(a) 2lx (b)

2lx

(c) 2lx (d) 0x

63. The centre of mass of a non-uniform rod of

length l whose mass per unit length 2kx

L,

where k is a constant and x is the distancefrom one end, is

(a) 34L (b) 8

L

(c) kL (d) 3k

L64. Two blocks of equal mass m are connected by

an unstretched spring and the system is kepton a friction less horizontal surface. A constantforce F is applied on the first block pulling itaway from the other as shown in the figure.Then the displacement of the centre of massat time t is

m m F

(a)2

2Ftm

(b)2

3Ft

m

(c)2

4Ft

m(d)

2Ftm

65. In the arrangement shown in the figure2Am kg and 1Bm kg . String is light and

inextensible. The acceleration of centre of massof both the blocks is

A

B

(a) 3g

(b) 9g

(c) g (d) 2g

66. Two blocks of mass m and 2m are kept onasmooth horizontal surface. They are connectedby an ideal spring of force constant k. Initiallythe spring is unstretched. A constant force isapplied to the heavier block in the directionshown in the figure.

m 2m F

Suppose at time t displacement of smaller blockis x, then the displacement of the heavier blockat this moment would be

(a)2x

(b)2

6 3Ft x

m

(c)3x

(d)2

6 2Ft x

m

67. Two blocks of mass 3 kg and 6 kg respectivelyare placed on a smooth horizontal surface. Theyare connected by a light spring of force constantk = 200 N/m. Initial the spring is unstretched.The indicated velocities are imparted to theblocks. The maximum extension of the springwill be

1.0 m/s

3kg 6kg

2.0 m/s

(a) 30 cm (b) 25 cm

(c) 20 cm (d) 15 cm

68. A metre ruler weighing 100 g rests on a tablewith a part projecting over the edge. The lengthof the part projecting out if a 5g body hung atthe end just tilts the ruler is(a) 37.5 cm (b) 26.8 cm(c) 40.2 cm (d) 47.6 cm

69. A man of mass m moves with a constant speedon a plank of mass M and length L kept initiallyat rest on a frictionless horizontal surface,from one end to the other in time t. The speedof the plank relative to ground while man ismoving is


66

(a)L Mt m

(b)L mt M m

(c)L Mt M m

(d) none of these

70. Two blocks of equal mass are tied with a lightstring, which passes over a massless pulleyas shown in figure. The magnitude ofacceleration of centre of mass of both theblocks is : (Neglect friction everywhere)

60° 30°

(a)3 14

g

(b) ( 3 1)g

(c) 2g

(d)3 1

2g

71. Two particles of equal mass m are projectedfrom the ground with speeds 1v and 2v atangles 1 and 2 as shown in figure. Thecentre of mass of the two particles :

v1 v2

1 2

m m

(a) can move in a vertical line

(b) can move in a vertical line

(c) can move in a horizontal line

(d) will move in a straight line for any valuesof 1 2 1, ,v v and 2

72. A small sphere of radius R held against theinner surface of a smooth spherical shell ofradius 6R as shown in figure. The masses ofthe shell and small spheres are 4M and Mrespectively. This arrangement is placed on asmooth horizontal table. The small sphere isnow released. The x-coordinate of the centreof the shell when the smaller sphere reachesthe other extreme position is

(a) R y

xO

(b) 2R

(c) 3R

(d) 4R

73. Two particles of masses m1 and m2 initiallyat rest start moving towards each other undertheir mutual force of attraction. The speed ofthe centre of mass at any time t, when theyare at a distance r apart, is

(a) Zero (b)1 2

2 1

1.m m

G tmr

(c)1 2

2 2

1.m m

G tmr

(d)

1 22 1 2

1.m m

G tm mr

74. Three identical spheres, each of mass 1 kgare kept as shown in figure, touching eachother, with their centres on a straight line.If their centres are marked P, Q, Rrespectively, the distance of centre of massof the system from P is

(a) 3PQ PR QR (b) 3

PQ PR

(c) 3PQ QR (d) 3

PR QR

75. Which of the following points is the likelyposition of the centre of mass of the systemshown in figure


67

(a) A (b) B

(c) C (d) D

76. Three masses of 2kg, 4kg and 4kg are placedat the three points (1, 0, 0), (1, 1, 0) and (0,1, 0) respectively. The position vector of itscenter of mass is

(a) 3 4ˆ ˆ5 5

i j (b) ˆ ˆ(3 )i j

(c) 2 4ˆ ˆ5 5

i j (d) 1 4ˆ ˆ5 5

i j

77. Look at the drawing given in the figure whichhas been drawn with ink of uniform line-thickness. The mass of ink used to draw eachof the two inner circles, and each of the twoline segments is m. The mass of the ink usedto draw the outer circle is 6 m. Thecoordinates of the centres of the different partsare : outer circle (0, 0), left inner circle(–a, a), right inner circle (a, a), vertical line(0, 0) and horizontal line (0, –a). The y-coordinate of the centre of mass of the inkin this drawing is

x

y

(a) a/10 (b) a/8

(c) a/12 (d) a/3

78. A T shaped object with dimensions shown inthe figure, is lying on a smooth floor. A force‘ F

’ is applied at the point P parallel to AB,such that the object has only the translationalmotion without rotation. Find the location ofP with respect to C

(a) 43

l

(b) l

(c) 23

l

(d) 32

l

79. Consider a system of two particles havingmasses m1 and m2. If the particle of mass m1is pushed towards the centre of mass ofparticles through a distance d, by whatdistance would be particle of mass m2 moveso as to keep the centre of mass of particlesat the original position

(a) 1

1 2

m dm m (b) 1

2

m dm

(c) d (d)2

1

mdm

80. If linear density of a rod of length 3m variesas = 2 + x, then the position of the centreof gravity of the rod is

(a) 73

m (b) 127

m

(c) 107

m (d) 97

m

81. Two masses m1 and m2 (m1 > m2) areconnected by massless flexible andinextensible string passed over massless andfrictionless pulley. The acceleration of centreof mass is

(a)2

1 2

1 2

m mgm m

(b)1 2

1 2

m mgm m

(c)1 2

1 2

m mgm m

(d) Zero

82. Three bricks each of length L and mass Mare arranged as shown from the wall. Thedistance of the centre of mass of the systemfrom the wall is

(a) L/4 (b) L/2

(c) (3/2)L (d) (11/12)L


68

83. A carpet of mass m made of inextensiblematerial is rolled along its length in the formof a cylinder of radius r and kept on a roughfloor. The decrease in the potential energy ofthe system, when the carpet is unrolled to aradius 2

r without sliding is (g = accelerationdue to gravity)

(a) 34

mgr (b) 58

mgr

(c) 78

mgr (d) 12

mgr

84. The density of a non-uniform rod of length 1mis given by (x) = a(l + bx2) where, a and bare constants and 0 x 1. The centre ofmass of the rod will be at

(a)3(2 )4(3 )

bb

(b)

4(2 )3(3 )

bb

(c)3(3 )4(2 )

bb

(d)

4(3 )3(2 )

bb

85. A spherical cavity of radius r is carved outof a uniform solid sphere of radius R as shownin the figure. The distance of the center ofmass of the resulting body from that of thesolid sphere is given by

(a) 2R r

(b) 0R

r

(c) 2R r

(d)3

2 2r

R Rr r

86. Two masses m1 and m2 are connected by amassless spring of spring constant k andunstretched length l. The masses are placedon a frictionless straight channel which weconsider our x - axis. They are initially at restat x = 0 and x = l, respectively. At t = 0, avelocity of v0 is suddenly imparted to the firstparticle. At a later time t0, the centre of massof the two masses is at.

(a)2

1 2

m lx m m

(b) 2 01

1 2 1 2

m v tm lx m m m m

(c)2 2 0

1 2 1 2

m l m v tx m m m m

(d)2 1 0

1 2 1 2

m l m v tx m m m m

87. Two uniform plates of the same thickness andarea but of different materials. One shapedlike an isosceles triangle and the othershaped. Like a rectangle are joined togetherto form a composite body as shown in thefigure. If the centre of mass of the compositebody is located at the midpoint of theircommon side, the ratio between masses ofthe triangle to that of the rectangle is

(a) 1 : 1 (b) 4 : 3

(c) 3 : 4 (d) 2 : 1

88. The distance between the vertex and thecenter of mass of a uniform solid planarcircular segment of angular size and radiusR is given by

(a)sin( /2)4

3R

(b)sin( /2)R

(c)4 cos3 2

R

(d) 2 cos( )3

R

89. A smaller cube with side b (depicted by dashedlines) is excised from a bigger uniform cubewith side a as shown below such that bothcubes have a common vertex P. LetX = a/b. If the centre of mass of theremaining solid is at the vertex O of smallercube then X satisfies


69

(a) X3 – X2 – X – 1 = 0(b) X2 – X – 1 = 0(c) X3 + X2 – X – 1 = 0(d) X3 – X2 – X + 1 = 0

90. A thin rod of length ‘L’ lying along the x-axiswith its ends at x = 0 and x = L. Its linear

density (mass/length) varies with x as nxk

L

,where n can be zero or any positive number.If the position xcm of the centre of mass ofthe rod is plotted against ‘n’ which of thefollowing graphs best approximates thedependence of xcm on n

(a) (b)

(c) (d)

4. INTEGER TYPE QUESTIONS91. A body projected with a speed u at an angle of

60o with the horizontal explodes in two equalpieces at a point where its velocity makesan angle of 30o with the horizontal for 1sttime. One piece start moving verticallyupward with a speed of u/23 after explosion.What is velocity of one piece with respect toother in the vertical direction just after theexplosion?

92. In an at wood machine the two blocks havemasses 1 kg and 3 kg. The pulley is masslessand frictionless and string is light. Theacceleration of the centre of mass (in m/s2)of this system is 0.5 x. Find the value of x.

93. A body of mass 5/6 kg kept at rest in

horizontal plane is acted upon by a variableforce given by F = 5e–t newton in the samehorizontal plane. Find the terminal velocityattained by the body.

94. A ball is projected from ground with a speed70 m/s at an angle 45o with the vertical sothat it strikes a vertical wall at horizontaldistance 490/3 m from the point of projection.If the ball returns back to the point ofprojection without any collision with groundthen the coefficient of restitution between theball and wall is e, then find the value of(1/e)2.

95. Velocity of a particle of mass 2 kg varies withtime t according to the equation ˆ ˆ(2 4 )v t i j

m/s. Here t is in seconds. Find the magnitudeof impulse (in N-s) imparted to the particle inthe time interval from t = 0 to t = 2s.

96. Three balls A, B and C are placed on a smoothhorizontal surface. Given that mA = mC = 4mB.Ball B collides with ball C with an initialvelocity v as shown in figure. Find the totalnumber of collision between the balls. Allcollisions are elastic.

A B Cv

97. A thin uniform sheet of metal of uniformthickness is cut into the shape bounded bythe line x = a and y = ± kx2, as shown. Thecoordinates of the centre of mass is (a/, 0),what is the value of + ?

y=kx2

y=–kx2

a x

y

98. Seven homogeneous bricks, each of lengthL, are arranged as shown in figure. Each brickis displaced with respect to the one in contactby L/10. The x coordinate of the centre of massrelative to the origin O shown is x0, what isthe value of 70 /11L x0 ?

O X


70

1. CONSERVATION OF MOMENTUM1. c 2. a 3. d 4. a 5. b6. c 7. b 8. c 9. c 10. b11. b

2. COLLISSION12. d 13. a 14. b 15. d 16. d17. d 18. c 19. d 20. d 21. a22. a 23. a 24. a 25. c 26. c27. d 28. a 29. b 30. a 31. c32. b 33. d 34. d 35. b 36. a37. c 38. a 39. c 40. b 41. a42. d 43. d 44. b 45. b 46. a47. c 48. d 49. b 50. b 51. d52. a 53. c 54. b 55. c 56. b57. d 58. c

3. CENTRE OF MASS59. b 60. d 61. a 62. c 63. a64. c 65. b 66. d 67. a 68. d69. b 70. a 71. b 72. b 73. a74. b 75. c 76. a 77. a 78. a79. b 80. b 81. a 82. d 83. c84. a 85. d 86. d 87. c 88. a89. a 90. d

4. INTEGER TYPE QUESTIONS91. (0) 92. (5) 93. (6) 94. (4) 95. (8)96. (2) 97. (7) 98. (4)

Documents

Topper’s Package Physics - XI Conservation of Momentum ......2020/07/21 · Topper’s Package Physics - XI Conservation of Momentum and Centre of MassPermutation and Combinations