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SCHOLASTIC APTITUDE TEST 1995.

PHYSICS

Section I 10 Marks

Section II 20 MarksSection III 15 Marks

Section IV 15 Marks

SECTION I

1. Velocity of light in centimeter per nanosecond is _______________________ .2. Phase of vibrating particles varies linearly and continuously when a wave travels in a

medium. The linear distance between particles differing in phase by p when a wave offrequency 2 kHz travels at 350 m/s is a medium is __________________.

3. Density and youngs modulus of a certain hypothetical material are 5 gm/cm3 and

2.0 x 1010

Pa. Velocity of sound wave in this material is ______________.4. Field strength at a certain distance from a charge Q is E. Field strength at one fourth ofthis distance from a charge Q/4 is _______________ .

5. Farad x Ohm expressed in the simplest form equals _________________.6. A conductor carries a current vertically upwards. Magnetic field due to this current to the

East of the conductor would be directed ____________________________.7. An electron is moving southward in a region of space having a magnetic field directed

vertically upwards. It experiences a force towards _________________ .8. The change that takes place in the nucleus when a beta particle is emitted is

________________.9. Two Deutrons combine to form a Helium nucleus. The masses of Deuterium and Helium

atoms are 2.0141 u and 4.0026 u respectively. The energy yield in MeV per reaction is________________.10. Electromagnetic radiations of wavelength 5 nm fall in the _________________ region.

SECTION II

1. A man moves 100 m 30 East of south then another 100 m 60 North of East. He is at adistance of _________________ from the starting point.

2. Displaced air exerts a vertcally upward force equal to its own weight on a body. Forceexerted by the displaced air on a man of weight 60 kg is nearly __________________ .

( Average density of a human being is nearly same as that of water and density of air is1.3 gm/l. ).3. A mirror produces a magnified image of a linear object placed 30 cm away from it 30 cm

away from the object. If the object is moved towards the mirror by 5 cm the image movesby ____________.

4. With velocity of light in vaccum chosen as a standard the refractive indicies of water andglycerine are 4/3 and 8/5 respectively. If velocity of light in water is chosen as standardrefractive index of glycereine would be ___________________ .

5. A source of sound of frequency 5 kHz is moving at 20 m/s. The wavelength of waves infront of the source is _______________________ .( Velocity of sound in air is 350 m/s ).

6. Two wires of circular cross section are made of equal amounts of same material and have

their radii in the ratio 1:2. The ratio of their electrical resistances is___________________.

7. Current betweenjunctions A and B is_______________ .

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8. ABCDEFGH is awireframe of twelveconductors forming theedges of a cube. Resistancebetween any two adjacentcorners is R. If theconnection between A,Eand C,G are removed theeffective resistancebetween B and D would be________________.

9. A battery is rated 12 V and has a capacity of 12 Ah. ( 1 Ah means the battery can driveone ampere of current for one hour or half ampere for two hours and so on..... ). Theenergy it can deliver is _______________________.

10. An electric lamp is rated 40 W at 200 V. If the lamp is operated at 150 V its power wouldbe _____.

SECTION III

The amount of heat Q flowing along the length of a rod in a time t is given by the expression

Where q 2 and q 1 are temperatures of hot and cold ends, A and L are area of cross section andlength of the rod, and K the coefficient of thermal conductivity ( a constant for the givenmaterial ) of the rod. It is assumed that there is no heat loss from the sides of the rod.

1. A rod is 50 cm long and has a cross sectional area of 10 mm2. If coefficient of thermalconductivity of the material of the conductor is 400 W/mK, the rate of heat flow alongthe rod is _____________________.

2. Temperature gradient is the rate at which the temperature varies with the length of the rodand is a constant for a rod carrying heat in steady state. If the temperature gradient of arod is 5 K/mm, the heat that flows in one minute through a rod of cross sectional area2 cm2 and coefficient of thermal conductivity 250 W/mK is equal to________________.

3. When two rods are placed end to end the rate of heat flow in them must be same. If tworods of equal areas of cross section and having their lengths and coefficients of thermal

conductivities in the ratio 1:2 and 2:1 respectively have their free ends maintained at350 K and 300 K respectively, the temperature of the junction will be _______________.

4. The amount of heat that escapes from a house through a 3 m x 2 m glass window pane ofthickness 5 mm for a temperature difference of 10 C in one hour is____________________. ( Coefficient of thermal conductivity of glass is 0.008 W/cmK )

5. One end of rod of cross sectional area 5 cm2, length 25 cm, coefficient of thermalconductivity 210 W/mK is maintained at 100 C and the other end is connected to beakerof water containing melting ice. The amount of ice that melts in a minute is_______________. ( Latent heat of fusion of ice is 80 cal/gm )

SECTION IV

A body floats when the weight of the liquid it displaces equals its own weight. Questions in thefollowing section are based on this principle.

1. A block of ice (density 900 kg/m3) is floating in a beaker of liquid (density 1200 kg/m3).The fraction of its volume seen above the liquid is ____________________ .

2. A body of density 1200 kg/m3 just floats in a homogenous mixture of two liquids ofdensities 1000 kg/m3 and 1500 kg/m3. The ratio by volumes in which the liquids aremixed is ____________________ .

3. A cubical block of Aluminum has a cavity inside. If it floats in water with 7/8 of itsvolume submerged in water. The ratio of the volume of the material to the ratio of its

external volume is __________________ .

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4. A cubical block C floats as shown with one fourthof its volume submerged in liquid A and theremaining three fourths in liquid B as shown. Ifdensity of liquid A is 600 kg/m3 and that of B is400 kg/m3, density of the material of the block is_____________________.

5. A test tube containing some lead shot floats vertically in a beaker of water. A few leadshots are removed from the tube and dropped in to the beaker. The level of water in thebeaker _______________ .( Assume that the test tube continues to float vertically afterthe lead shots are removed from it ).


Section A 10 Marks Section B 20 Marks Section C 30 Marks

SECTION A

1. A large amount of ice at 0 C is added to a beaker of water at 30 C. Some of the icemelts and the rest floats on water in the beaker. The temperature of the water in thebeaker is .

2. The angle of minimum deviation of an equiangular prism is equal to the angle of theprism. The refractive index of the material of the prism is

.3. A wave of frequency 170 Hz travels through a narrow pipe closed at one end where it is

reflected. The reflected wave and the incident wave interfere forming a stationary wavein the pipe. If the nearest antinode in the pipe is 50 cm from the closed end, the velocityof the wave is .

4. For compressions and rarefactions to form in a medium the direction of vibration of the

particles and the direction of propagation of the wave must be .

5. When a person speaks in to a microphone the vibrations of its diaphragm are free/resonant/forced . ( Mention the correct answer in your response sheet )

6. A current of 3.2 mA is flowing through a wire. The number of electrons crossing anysection of the conductor in a minute would be .

7. A long wire has electronic current flowing through it from north to south. The north poleof a compass needle placed above the wire would deflect towards .

8. A filament lamp is rated 100 W at 200 V. The filament is cut in to two equal parts and

one of them is used at 250 V. Its power would be .

9. A hypothetical radioactive nucleus emits a proton and a deuteron in succession. The massnumber and charge number of the product nucleus are reduced by and

respectively.

10. When aluminum is bombarded with alpha particles, the resulting nucleus becomesradioactive and emits particles.

11. With x axis westward and y axis southward the coordinates of two places are 150 m,200 m and 450 m, 600 m.

The westward distance between the places is .The southward distance between the places is .The distance between the places is .

12. A solid is heated by a source supplying heat at a constant rate. The temperature at firstrises from 20 C to 80 C in 5 minutes and then remains steady for 60 minutes before itstarts rising again. The ratio of specific heat of the solid to its latent heat of fusion is

.13. A concave mirror is kept some distance away from a wall. A twice magnified image is

formed on the wall when an object is placed between the mirror and the wall at a distanceof 30 cm from the wall. The focal length of the mirror is .

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14. In the expressionv, E and D denote velocity, Elasticity and density. Then a and b are equal to and

respectively.15. Charge stored by a condenser is 5 mC when a potential difference of 2 V is maintained

between its plates and the plates have a material of dielectric constant 5 between them.Charge on the plates when the potential difference is doubled and the material between

the plates is replaced by material of dielectric constant 2 would be .

16. A cell drives a certain charge through a circuit in a certain time. Due to a change in theresistance of the circuit in which this cell is a part the same charge takes twice greatertime to be driven. Work done in the first and second cases by the cell are in the ratio

.17. A charged liquid is flowing through a pipe of cross sectional area a. Unit volume of this

liquid has a charge q. If the velocity of the flow is v, current through any section of thepipe is .

18. Two wires are made of equal mass of same material and have their cross sections in theratio 3:4. Their resistances will be in the ratio .

19. To raise the temperature of 10 liters of water through 20 C a 1000 W heater wouldrequire minutes.

20. A length of wire is made in to circular coil with certain number of turns. For a certaincurrent through it the magnetic field at its center is X. If another coil made of samelength of wire has twice greater number of turns, magnetic field at its center for samecurrent as the first coil would be .

SECTION C

21. The distance of a particle moving along a straight line from another stationary point on

the same line is given by l = 2+ 4t + 5 t

2

with l in meters and t in seconds. The distancetravelled by the body between 4 th and 6 th seconds will be .

22. Two cars are travelling on a straight road with the one car 200 m from the other at thesame speed. At a certain moment brakes are applied to the rear car and it deceleratesuniformly travelling 20 m before coming to rest. The distance between the cars at themoment the rear car comes to rest is .

23. Two points A and B are located on the floor of a room 30 cm and 20 cm away from awall. The distance between the points parallel to the wall is 50 cm. An insect is at Amoving on the floor at 5 cms1. It has to first reach a point C on the wall and then reach Bsuch that AC and BC make equal angles with normal to the wall at C The time taken forthis motion would be .

24. Two particles are going round concentric circular paths making 30 RPM and 60 RPM.the time interval between their being at the minimum and maximum distances is

.25. A wooden block of certain volume is floating in water with a metal block of one eighth

its volume hanging from below it. The volume of the submerged portion of the woodenblock is one fourth its total volume. When the metal block is placed on top of the woodenblock, the volume of the submerged portion of the wooden block is three fourths its totalvolume. The ratio of densities of wood and metal is .

26. Intensity of light at a point is proportional to square of the distance of the point from asource of light. A source of light is at a height of 30 cm above the center of a circulartable of radius 40 cm. The ratio of intensities at the center and the edge of the table is

.27. Two points on a thin circular ring are located such that the radial lines joining them to the

center have a certain angle between them. When this angle is 90 the electrical resistanceoffered by the ring for a current entering one point and leaving the other is R. Theresistance when the angle is 60 will be .

28. An electron moving vertically upward in a horizontal magnetic field experiences a forcedirected towards east. The force experienced by an electron travelling eastward in thismagnetic field will be directed towards .

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29. Radii of circular paths of electrons round the nuclei are proportional to the square ofquantum numbers. If square of time taken to go round circular path once by an electron isproportional to cubes of the radius, The ratio of frequencies of revolution in orbits ofquantum numbers 1 and 4 is .

30. Mass of a radioactive substance at a certain moment is 16 gm and its half life is 2 hrs.The mass of the substance that disintegrates in 1 hour is greater than / equal to / lessthan 4 gm. ( Mention the correct answer in your response sheet and justify your answer)


Section A 10 Marks Section B 20 Marks Section C 30 Marks

Useful Physical constants:

i. acceleration due to gravity = 10 ms2

ii. Charge of electron e = 1.6 x 10-19 Ciii. 1/4p e o = 9 x 109 Nm2C2iv. Density of wood = 0.5 gm/cc

SECTION A

1. A wire carries a current vertically downwards. The magnetic field to the East of the wireis directed towards .

2. A source of sound is moving at 36 kmph straight towards an observer moving away fromit at 36 kmph and along the same straight line. The frequency of the source is 400 Hz.Frequency of the note received by the observer is .

3. If 0.16 mA of current is flowing through a wire, the number of electrons crossing anysection of the wire in a minute is .

4. A hypothetical radioactive nucleus emits a proton and a positron. Its mass numberdecreases by and its charge number decreases by .

5. Mass equivalent of energy of 186.2 MeV is amu.6. In electrolysis of copper sulphate solution, an alternating current source is used. The mass

of copper deposited on the cathode plate is .7. In wavelength of a wave in a certain medium is 20 cm and its velocity is 350 m/s. Its

wavelength in a medium where the velocity is 1400 m/s would be equal to.

8. The energy consumed by a 20 W lamp used for 25 hrs is kWh9. If a cell of emf 6 V drives a current of 2 amp through a circuit for 10 minutes, the amount

of work done by it is .

10. 20 mJ of work is done in moving one micro Coloumb of charge between two points. Thepotential difference between these points is .

SECTION B

1. Light travels at v1 in a medium and at v2 in another medium. The ratio of refractiveindices of the media is .

2. The closest distance between particles one at an extreme position and another at theequilibrium position is 2 m. If the frequency of this wave is 2.5 kHz, the velocity of thewave is .

3. At 1 atmosphere pressure and a certain temperature the velocity of sound is 350 m/s. At 2

atmosphere pressure and same temperature the velocity would be .4. Two stones are released from rest one from a height of 9 m and another from some

unknown height above the ground. One of the stones hits the ground 1 s after the otherstrikes the ground. The height from which the second stone is released can have values of

.5. Light falling on a sphere made of a photoelectric material causes it to lose electrons. If a

sphere initially uncharged has acquired a charge of 3.2 m C, the number of electrons ithas lost is .

6. Energy stored by a capacitor is given by the expression . If a 5 m Fcapacitor charged to 200 V, the energy it possesses is equal to .

7. 2 kgf/cm2

= N/m2

.( kgf = g N )8. Momentum is mv and kinetic energy is mv2/2. A body of mass 4 kg has a kinetic energyof 32 J. Its momentum is .

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9. A solid object A of mass 200 gm object placed in contact with a source supplying heat ata constant rate undergoes a rise in temperature of 20 C in 40 s. Another solid object B ofmass 300 gm needs 20 s for a 5 C rise in temperature. The ratio of specific heats of Aand B is .

10. Mass of a radio active substance at a certain moment is 16 gm. The mass of it thatdisintegrates in its third half-life period is .

SECTION C

In some of the following questions information ( A new rule, a new equation) required toanswer the questions is provided. Read the information provided carefully and answer thefollowing question. The questions can be answered by proper appreciation of the informationprovided.

1. Resultant R of two parallel forces P and Q acting at A and B is equal to P+Q and the pointC where it acts can be located from the relation P(AC)=Q(BC). ( Refer to the figureshown below )

The resultant of two parallel forces is 40 N and acts 10 cm from the force of 10 N. The otherforce acts at a distance of from the 10 N force.

2. A stone projected in to the air from the ground level with a velocity v directed at q above

the horizontal hits the ground at a horizontal distance of from the pointof projection. The maximum height attained by it during the flight is given by the

expression .

A projectile hurled at 45 attains a maximum height of 25 m. The horizontal distance ittravels before it strikes the ground is .

3. A positively charged particle travelling vertically upwards experiences a northward force

due to magnetic field directed at right angles to it. A negatively charged particletravelling northward in the same magnetic field will experience a force.

4. A long uniform wooden stick of cylindrical cross section is weighted at the bottom suchthat a length of 20 cm of it protrudes out of water as it floats vertically. If a length of 10cm is sawed off from the stick and it is floated again, the length that protrudes above thewater surface would be .

5. A lens forms a twice magnified image of an object kept 30 cm away from it on onesideon a screen kept on the other side. Without disturbing the object, the lens is movedthrough 5 cm towards the object, the screen must be moved by toobtain a sharp image.

6. Between any two adjacent junctions theresistance of a wire frame shown is same. Ifthe resistance between B and E is R,resistance between A andB is .

7. An insect is located at the edge of a fan blade of length 40 cm. It starts walking towardthe centre of the fan. As the insect moves 10 cm from its initial position, the blade hasturns through a right angle. The distance between initial and final positions is

.8. Two cars are travelling towards a junction along two different intersecting roads. One of

them is 200 m away and is moving uniformly at 10 m/s. The other located 100 m away

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starts from rest and accelerates uniformly at 2 m/s2 towards the junction. The intervalbetween the moments when the cars pass the intersection is .

9. A wire is of square cross section of side a and length L and has a resistance R. Anotherwire made of same material and of twice greater length has the same volume as the first.The electrical resistance of the second wire is .

10. A ring with a uniformly distributed charge (Q) of radius R repels a point charge (q)

placed on its axis with a force F given by the expressionwhere x is the distance of q from the centre of the ring.

A point charge of 5 m C is located on the axis of a ring of radius 60 cm carrying a charge of40 m C. The distance between any point on the ring and the point charge is 100 cm. The forceexperienced by the point charge is .

SCHOLASTIC APTITUDE PHYSICS 1998

Useful Physical constants:

I. Plancks constant = 6.6 x 10-34 Js Velocity of Light c = 3 x 108 m/sII. Electron Volt = 1.6 x 10-19 J Relative density of cork = 0.25

SECTION A

1. What temperature change on the Kelvin scale is equivalent to a 10 degree change on theCelsius scale?A) 283 KB) 273 KC) 18 KD) 10 KE) 0

2. A light year is a unit of

A)acceleration

B)distance

C)speed

D)time

E)velocity

3. The critical angle of a material is the angle of incidence for which the angle of refractionis: A) 0 B) 30 C) 45 D) 90 E) 180

4. A plane mirror produces an image that is:A) real, inverted, and larger than the object.B) real, upright, and the same size as the object.C) real, upright, and smaller than the object.D) virtual, upright, and the same size as the object.

5. An object is located 0.20 m from a converging lens which has a focal length of 0.15 m.Relative to the object, the image formed by the lens will be:A) real, erect, and smaller. B) real, inverted, and smaller.C) real, inverted, and larger. D) virtual, erect, and larger.

6. If the frequency of sound is doubled, the wavelength:A) halves and the speed remains unchanged.B) doubles and the speed remains unchanged.C) is unchanged and the speed doubles.D) is unchanged and the speed halves.

7. When metal rod 1 is placed in contact with metal rod 2, thermal energy flows from 1 to 2.A possible explanation is that 1 has a higherA) specific heat B) heat capacity C) mass D) temperature E) Density

8. When the velocity of a moving object is doubled, another physical quantity associatedwith the object also gets doubled. This quantity isA) acceleration B)kinetic energy C) mass D) momentum E) Potential Energy

9. Which of the following could NOT be used to indicate a temperature change? A changein: A) color of a metal rod. B) length of a liquid column.C) electrical resistance. D)mass of one mole of gas at constant pressure.

10. Two charges repel each other with a force F when they are a certain distance apart. Thecharges are halved and the distance between them is also halved. The force between thecharges now is

A) F/16 B) F/4 C) F/8 D)F E) F/2

SECTION B

11. A mass m of helium gas is in a container of constant volume V. It is initially at pressure pand absolute temperature T. Additional helium is added, bringing the total mass of

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helium gas to 3m. After this addition, the temperature is found to be 2T. What is the gaspressure?

A) 2 /3 p B) 3 /2 p C) 2 p D) 3 p E) 6 p12. Which would be the most comfortable temperature for your bath water?A) 0o C B) 40 K C) 110o C D) 310 K E) 560 K

13. A wire of length 50 cm has a mass of 20 gm. If its radius is halved by stretching, its new

mass per unit length will beA) 0.4 gm/cm B) 0.2 kg/m C) 2 kg/m D) 0.1 gm/cm E) 0.2 gm/cm14. A string is tied around a cork of mass m and the free end of the string is attached to the

bottom of a water-filled container with the cork totally immersed in the water. Thetension in the string is:

A)0 B) mg C) 2 mg D) 3 mg E) 4 mg15. A long straight wire conductor is placed below a compass. When the conventional current

in the conductor is from south to north and large, the N pole of the compass:

A) remains undeflected. B) points to the south.C) points to the west. D) points to the east.

E) has its polarity reversed.16. A beam of light passes from medium 1 to medium

2 to medium 3 as shown in the accompanyingfigure. What is true about the respective indices ofrefraction (n1, n2, and n3)?A) n1 > n2 > n3 B)n1 > n3 > n2C) n2 > n3 > n1 D)n2 > n1 > n3E) n3 > n1 > n2

17. A positively charged conductor attracts a second object. Which of the followingstatements could be true?I. The second object is a conductor with negative net charge.

II. The second object is a conductor with zero net charge.III. The second object is an insulator with zero net charge.

A) I only B) II only C) III only D) I & II only E) I, II & III18. A ray of light is directed toward a point P on a

boundary ( represented by the dotted line ) as shownto the right. Which segment best represents therefracted ray?

A) PA B) PBC) PC D) PD E) PE

19. A book is placed on a table. Let FEB be force exerted by earth on the book, FTB be forceexerted by table on the book, FBT be force exerted by book on the table and FBE be forceexerted by book on the earth. Among these forces, the action, reaction pairs are

A) FEB , FTB B) FBE , FTB C) FEB , FBE D)FEB , FBT E)FBE , FBT20. You are given three 1.0 W resistors. Which of the following

equivalent resistances CANNOT be produced using all three resistors?

A)1 /3 W B) 2 /3 W C) 1.0 W D) 1.5 W E) 3.0 W

SECTION C

21. Two cars are travelling in the same direction at 60 kmph and are 30 km apart. A third cartravelling at 30 kmph crosses one of the cars at a certain moment. Find the time elapsedbefore it crosses the second car. Solve the problem if the first two cars are travelling inthe opposite directions.

22. A point object is located at a distance of 30 cm on the principal axis of a convex lens offocal length 20 cm. If the lens is moved away from the object by 10 cm, find the distancethrough which the image moves.

23. From amongst resistances of 2 W ,3 W ,6 W and 7 W , two resistors are picked andcombined first in series and then in parallel. Their equivalent resistances are found to be 2

W and 9 W . Find the parallel equivalent of the remaining two resitances.

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24. Which of the following is NOT possible for the imagesformed by the lens in the accompanying figure?A) real and invertedB) real and smaller in sizeC) real and larger in sizeD) virtual and erectE) virtual and smaller in size

25. A cyclist covers a certain distance in 50 minutes riding his bicycle at a certain speed andin 40 minutes riding at a faster speed. If he rides his bicyle changing his speed from lowerto higher speed every ten minutes how long would he take to cover the distance. Considerboth the cases that arise.

26. A horse running along a 5 m wide circular track takes p seconds more to travel along theouter edge than the time taken to travel the inner edge. Find the speed of the horse.

27. In a certain process initial energy of the system is -13.6 eV and final energy is - 3.4 eV.

The enegy loss is due to the emission of a quantum of light by the system. If the energyof the quantum of light is given by E=hn , where h is the Plancks constant and n is thefrequency of the light, Find the wavelength of light emittted.

28. A metallic sheet of length L, width W and some thickness is melted and formed in to ahollow cylinder. If the inner and outer radii of the cylinder are a and b respectively, andthe length of the cylinder is same as the width of the sheet, Find the thickness of thesheet.

29. Two convex lenses of focal lengths 20 cm and 30 cm are placed 50 cm apart coaxially. (i)A point object is located at a distance of 20 cm from the lens of shorter focal length. Therays of light from this object pass through the first lens and then through the second. Findthe distance where the rays of light converge from the second lens. (ii) If a parallel beam

of light were to be incident on the first lens and the rays refract a second time after firstconverging, find the distance where the rays converge after second refraction

30. In the circuit shown adjacent junctions areconnected by equal resistances. The effectiveresistance between junctions A and G when theresistances between junctions C,E and D,F areremoved is R. The removed resistances arereconnected and the resistances betweenjunctions B,D and F,H are now removed. Findthe new effective resistance between A and G.

SCHOLASTIC APTITUDE TEST 1999

1. At a certain moment of time a particle moving along a straight line is located at a distanceof 5 m from a point and at a subsequent moment it is at a distance of 10 m from the samepoint. The minimum and maximum distances the particle could have moved are

.2. A particle is going round a circular path with a constant speed. The angle between its

acceleration and velocity vectors is .3. An object placed on an equal arm balance requires 12 kg to balance it. When placed on a

spring scale, the scale reads 120 N. Everything (balance, scale, set of masses, and theobject) is now transported to the moon where the gravitational force is one-sixth that onEarth. The new readings of the balance and the spring scale arerespectively.

4. A body is thrown up from a certain height and another thrown down from the same pointwith the same speed at the same time. If they hit the ground with a time gap of 4 s, thespeed of projection is .

5. On applying brakes a car slows down from v1 to v2 as it travels a certain distance andfrom v2 to v3 as it travels an equal distance. the relation between the velocities is

.

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6. A ball of mass m is thrown vertically upward. Air resistance is not negligible. Assumethe force of air resistance has magnitude proportional to the velocity, and directionopposite to the velocity's. At the highest point, the ball's acceleration is

( greater than /less than /equal to) acceleration due to gravity.7. A converging lens with focal length +10 cm would produce a twice magnified image of

an object, if the object is placed at a distance of from it.8. Two small identical conducting spheres are separated by a distance much larger than their

diameter. They are initially given charges of -2.00 C and +4.00 C, and are found to exert a force on each other of magnitude 1 N. Without changing their position, they areconnected by a conducting wire. When the wire is removed, the magnitude of the forcebetween them is .

9. Three 60 W light bulbs are mistakenly wired in series and connected to a 120 V powersupply. Assume the light bulbs are rated for single connection to 120 V. With themistaken connection, the power dissipated by each bulb is .

10. In the circuit shown the resistance R1,R2, R3, R4 and R5 are 80 , 20 60

25 and 20 respectively. A current of 0.10 A flows through the 25

resistor shown in the diagram. Thecurrent through the 80 resistor is

.

11. A wire of a certain radius has a resistance R. Another wire of same length, same materialhas one end of same radius and the other end of twice greater radius, the radius increasing

linearly from the narrower end. If the resistance R' of the second wire is less than nRwhere n is an integer, n would be .

12. Angular momentum of a particle about a point is defined as the product of its mass,velocity and perpendicular distance from the given point. A particle of mass m is movingin the xy plane parallel to x- axis at a distance d from it with a speed v. Its angularmomentum about the origin would be

13. An alloy consists of a metal A of density 3.1 gm/cc and a metal B of density 8.8 gm/ccmixed in the ratio 2:1. A hollow ball made of this material has an external volume of 80cc and a mass of 100 g. The volume of the cavity is .

14. A body is dropped from a height of 20 m above the ground. If gravity disappears 1second after it starts falling , the time it takes to hit the ground is ( Assume acceleration

due to gravity = 10 ms2 ) .

15. The diagram to the right shows the velocity-time graph for two masses A and B thatcollided elastically.Consider the following statements.I. A and B moved in the same direction afterthe collision.II. The velocities of A and B were equal atthe mid-time of the collisionIII. The mass of A was greater than the mass

of B.The true statements from these are

.

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16. Potential difference between A and B isand the current flowing from

C to D is .

17. Parallel beam of light parallel to the principal axis of a lens falls on a lens of focal length50 cm. After passing through the first lens they pass through another coaxially mountedconvex lens of focal length 50 cm placed 150 cm from the first lens. After passingthrough the second lens, the rays converge at a distance of __________ from the firstlens.

18. If velocity of light in medium A is 2.25 10 8 m/s. Refractive index of medium B withrespect to medium C is 1.2. Velocity of light in a medium C is 1.5 108 m/s. Refractiveindex of A with respect to B is . ( You should not use the value ofvelocity of light in vaccum or air ).

19. Particles A and B are free to move along parallel paths. B is moving at a constant velocityof 10 m/s and A starts moving at the moment B passes it. If A accelerates at 1 m/s2 for 5 sand then travels at a constant velocity, the distance between A and B 10 s after B passesA is .

20. Dust particles are uniformly distributed in space with a mass per unit volume . Acircular plate of area A is moving in this space at v. The dust particles that come in tocontact with the plate stick to it. The mass of dust that collects on the plate in a time t is

.

21. 15 equal resistances (AB,BC,CD,.) are connected to form a staras shown. When the resistances JBand JH are removed the equivalentresistance between terminals A and Iis R. The equivalent resistancebetween A and I when theresistances AJ and JI are removedwould be .

22. A point object is located 5 cm above the principal axis of a lens of focal length 20 cm. Ifthe distance of the object measured parallel to the principal axis is 30 cm, the distance ofthe image of the object from the principal axis would be .

23. The orbital radius of a certain satellite is R and it takes two hours to complete onerevolution. The radius of the orbit of a satellite that would take 16 hours to complete onerevolution would be .

24. A longitudinal wave is normally incident on a wall and is reflected. The incident and thereflected waves interfere producing a stationary wave. If the nearest node to the wall is 25cm from it and the velocity of longitudinal waves in air is 350 m/s, the frequency of thewave is .

25. An solid object A has a mass m and is made of a material of density . One fourth of its mass is removed and another material of density /2 is added to it and a new solidobject B is formed. The mass of B is 5/4 times the mass of A. The difference in thevolumes of the two spheres is .

26. A sealed evacuated vessel of volume 1500 m3

and mass 3 105

kg is floating on water.The downward force that should be exerted on the vessel to just submerge it is.( Density of water is 1 gm/cc, assume g =10 m/s2)

27. A wagon of mass M is free to roll on frictionless rails and is located on a straight track. Aman of mass m is standing at one end of the wagon. The man runs parallel to the railstowards the other end and jumps off. If the speed of the man at the moment he jumps offis v, the speed of the wagon is .

28. Gravity at a height h above the earth is

for h

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for all d.( R= 6400 km, g is the gravity on the earth and g ' gravity at the specified position)Use these equations in filling the following blanks.

The height where the gravity is same as at a depth of 10 km isThe height where the gravity is same as at a depth of 3200 km is .29. The fundamental frequency of vibration of a string stretched between two supports is

given by the expression , where n, l, T and are the frequency, length ofthe string, tension in the string and mass per unit length respectively. Use this equation infilling the following blank.

A string stretched between two supports has a frequency n. This string is then stretched to twiceits original length and fixed between two new supports with same tension as earlier. The new

fundamental frequency is .

30. A charged particle moving northward at right angles to a magnetic field experiences aforce directed eastward. Another charged particle of opposite charge is moving towardssoutheast in the same magnetic field. The force experienced by it is directed towards

.

SCHOLASTIC APTITUDE TEST 2000

1. A body floats with half its volume submerged in a liquid A. The same body floats withthree fourth of its volume submerged in a liquid B. Equal masses of these two liquids aremixed to form a homogeneous mixture and the body is floated in this mixture again. Thefraction of the volume of the body that would be seen above the surface of the mixture is

.2. A line of cyclists separated by 50 m are travelling along a road at a constant speed of

4 m/s. Another cyclist is riding his bicycle at a constant speed of 6 m/s. The time taken byhim to cross 10 cyclists is if he is travelling in the same direction asthe others and if he is travelling in a direction opposite the others.

3. A particle starting from rest accelerates at 2 m/s2 for some time and then travelsuniformly and passes a point 175 m from the starting point 20 s after start. The velocities

of the particle at the moment of passing the 20th m and 30th m marks are and.

4. A body is dropped from a certain height. 2 seconds later another body is projectedvertically upward from the same point at 20 m/s. The distance between the first andsecond bodies 5 seconds after the projection of the second body is .( acceleration due to gravity = 10 ms2 )

5. A boy drops stones from the roof of a building on to the ground 9 m below. The firststone released by him strikes the ground at the moment he has just released the fifthstone. The second, third and fourth stones are at heights of ,and above the ground at this moment. ( acceleration due to gravity = 10 ms2 )

6. A pendulum has a time period of 2 s at a place where acceleration due to gravity is9.83 m/s2. To have the same time period of 2 seconds at a place where acceleration due togravity is 9.78 m/s2, it's length must be .

7. A beaker with negligible water equivalent contains some water of mass m. Some mass ofice at 0 c is added to this water. The mass of ice added being equal to half the mass ofwater in the beaker and all the ice added just melts. If half of this mass of ice were to beadded, the final temperature would have been .

8. Suppose gravitational force between two masses were to be given bywhere k is some constant. Two equal masses attract each other with a certain force whenthe distance is d. If each of the masses is doubled, the distance between them must beincreased times for the force to remain the same as earlier.

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9. If end correction is neglected it is possible to obtain resonance for lengths of air columnwhich are in the ratio 1:3:5:7: .. ( This ratio is an approximation ). A meter longtube with its lower end closed is held vertically. A vibrating tuning fork of frequency 480Hz is held at the mouth of the tube and water is slowly poured in to the tube. Shortest andlongest lengths of the water column for which resonance is obtained are and

. ( Velocity of sound in air is 345.6 m/s)10. A candle flame and a screen are 180 cm apart. A lens is placed between them. For a

certain position of the lens a twice magnified clear image is obtained on the screen. Thelens is now moved away from the candle through 30 cm. To obtain another clear imageon the screen, the distance through which the screen has to be moved isand the new magnification of the image is .

11. A ray of light incident normally on one face of an equiangular prism, gets internallyreflected from the second face and emerges through the base of the prism. The angle ofdeviation of the ray is . ( Draw a neat ray diagram. )

12. 110 Particles are chasing each other on a circular path of radius 7 m. The speed of anyparticle is 2 m/s. Number of particles crossing any radial line every second is

. If each of the particles carries a charge of 4 microColoumb, the averagecurrent in the path is .

13. All the resistances shown are equal. With resistance between A and D removed and theresistance between different points is measured. If the resistance between points B and Cis R, the resistance between points A and B would be

14. A potential difference applied to the ends of a wire causes a certain current to flowthrough it and a certain amount of heat to develop in it. The wire is stretched to obtain anew thin wire of half the original thickness. If the same potential difference is applied tothe ends of the new wire, the heat developed _______________ times and the currentflowing __________ times.

15. The current in a wire of resistance 10 Ohm varies as shown. The current remains constantfor one second and in the next second it is half of the value in the previous second. If theinitial value of the current is 8 A, the heat produced in the wire in 5 seconds is

joule, and the charge that flows across any section of the wire in thistime is .

16. A house uses 5 lamps of 40 W each for 5 hours a day and an electrical heater of 1000 W

for 1 hour a day. The energy consumed in a month of 30 days in kWh is .The mass ( in milligram ) that is equivalent to this energy is .17. Magnetic field produced by a circular coil of radius R and having N turns carrying a

current 'i'is given by . The magnetic field is perpendicular to the plane of thecoil and is directed out of the plane if the current is anticlockwise. Two concentric coilsmade of wires of same length 'L' are made in to coils of radii R and 2R and have samecurrent 'i' flowing through them in the same sense and are in the same plane. Themagnetic field at the center of the coils is . (Permeability of freespace o= 4 x 107 Hm1)

18. An electron starting from rest is accelerated through a potential difference of 182 V. Thekinetic energy (in joule ) gained by it is and it's velocity is .( mass of electron m = 9.1 x 10-31 kg, charge of electron e = 1.6 x 10 -19 C ).

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19. A charged particle moving south west at right angles to a magnetic field experiences aforce vertically upwards. This charged particle would not experience any force if itmoved in a direction .

20. B and C are constituents of a nucleus A. The binding energy of nucleus A having threenucleons of type B and four nucleons of type C in MeV is . (Mass of B =1.00733 amu, Mass of C = 1.00867 amu and Mass of A = 7.01586 amu)

PHYSICS -2001

Part A (6x5=30 Marks)

1. Two small stones are tied at the ends of a rope of length 5 m . Imagine you are holdingthem, one in each hand, with the rope hanging loosely on the top floor balcony of a tallbuilding. You release one stone at a certain moment and the other 0.5 s later along the

same vertical line from the same position. The rope will be taut after a time of. Assume that as the rope gets taut, the velocities of the stones becomes

equal to the average of the velocities of the stones just before the stone gets taut. Thevelocities of the stones 2 s later would be .

2. A concave mirror of focal length 25 cm and a convex lens of focal length 20 cm arearranged coaxially 85 cm apart. A point object is located on the principal axis of the

system 30 cm from the convex lens. Rays of light after passing through the lens fall onthe mirror and after reflection from the mirror pass through the lens again. These rays

converge at a distance of from the lens after passing through it a secondtime.

3. All Resistances are equal to 9 Ohm each.Equivalent resistance between B and C is

_________________ and the equivalentresistance between A and D when theresistances between GF and FE areremoved is _________________.

4. A cylindrical wire of radius R is made of two different materials. The inner portion ofradius R/2 is made of a material of resistivity r and the outer annular portion of thicknessR/2 is made of material of resistivity 2r . Resistance per unit length of this wire would be

.

5. A boat moves down stream a certain distance in a river. If the river were not flowing thetime taken would have been 2 hrs but with the river flowing the time taken is 1.5 hrs. Thetime taken to travel upstream the same distance would be .

6. Current flowing through a wire of resistance 2 Ohmvaries with time as shown. The amount of heatproduced and the charge that crosses a given sectionof the wire in 3 s would be and________________.

Part B (10x3=30 Marks)

7. Imagine a man moving from north pole to the equator and from the equator to the southpole, moving along the same longitude. The magnitude of the displacement in the firstand second parts are _____________ and ______________ and the total displacement is

____________.8. A chain is lying as a heap on a table. One end of it is pulled vertically upward with a

constant acceleration of 0.5 m/s2. The velocity of the mid point of the vertical portionwhen the upper end is at height of 0.64 m above the table is .

9. A carom striker hits a side of the carom board at some angle and rebounds. It then hits theadjacent side. The angle between the initial and final directions of motion is

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____________. (Assume the angles made by the line of motion with the normal beforeand after collision are same for both the collisions)

10. A thin circular tube of radius r has two openings at diametricallyopposite ends. A source of sound of frequency n is located at A.Sound travels along the paths 1 and 2 to B. The temperatures of airin 1 is higher than the temperature of air in 2 and thecorresponding speeds of sounds are v1 and v2 respectively. Thenumber of extra waves contained in one path as compared to otheris _________ _ . If a pulse of sound were to be emitted at A thetime interval between the moments the pulse arrives at B along thetwo paths to B is .

11. A sphere consists of inner portion of radius r made of a material of density 8 gm/cm3 ,and an outer layer of thickness t made of a material of density 4 gm/cm 3. This spherefloats in a liquid of density 10 gm/cm3 with half its volume submerged. The ratio r/t is

equal to _____________________.

12. The value of a resistance R can be determined by connecting it either as shown in Fig Aor as shown in Fig B. When connected as in A the readings are 2 A and 100 V and whenconnected as in B the readings are 2.1 A and 98 V. The resistance would lie between______________ and ______________. If the resistance of ammeter is 2 Ohm the valueof R is .

13. Sound wave of a frequency n travels in a certain gaseous medium with a velocity v. Asecond gaseous medium at same pressure as the first has twice greater density. The speed

of sound of frequency 2n in this medium would be .

14. A radio active substance of half life period 2 hrs is being produced in a reactor. At theinitial moment the mass of the substance is zero and production rate is 5 mg/s. The

substance is produced for 10 s. Two hours later the mass of the radioactive substancewould be nearly .

15. A negatively charged particle moving at right angles to a magnetic field in the southeastdirection experiences a vertical upward force. The force experienced by a positively

charged particle moving in the northwest direction would be .

16. Energy released in a fusion reaction of two Deuterons is nearly 24 MeV. Energy releasedin the fission of U235 is nearly 200 MeV. The mass of Uranium that should undergo

fission to release the same amount of energy as obtained by fusing nuclei contained in 1kg Deuterons would be and the energy released is .

PHYSICS - 2002

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1. A person leaves A at 6 AM, walks from A toB with a uniform speed of 4 kmph, from B toC at 6 kmph , C to B at 3 kmph and thenback to A at 4 kmph. If the time intervalbetween the moments he is at B is 90minutes and he was at C at 7 AM, Find thetime when he is returns to A.

2. Two stones are located at the same height above the ground at a horizontal distance of 20m. One of them is projected vertically upward at 20 m/s and the other dropped from rest

at the same moment. Find the distance between them one second later. (Assumeacceleration due to gravity is 10 ms2 )

3. A small mass of 2 kg is tied to the end of a string attached to a fixed point. The mass isdrawn aside such that the string is horizontal and is released. When it swings along acircular arc through an angle of 30o it has kinetic energy of 8 J. Find its kinetic energy

when the string becomes vertical.

4. A car is taking a turn of radius 20 m at a speed of 36 kmph. Find the ratio of resultantforce on the car to its weight.

5. A car starting from rest goes round a bend with its speed increasing linearly with time. If2 s after start its centripetal acceleration is 4 m/s2 find its centripetal acceleration a second

later.

6. A particle is going round a circular path making one revolution in 4 s. Consider anydiameter of the circle and project the position of the particle going round the circle on to

diameter. Times taken to move between two points on the circle and the time taken tomove between the corresponding projections on the diameter are obviously the same.

Find the time taken by the projection to move between the extreme of the diameter and apoint midway between the center and the extreme.

7. A particle starting from rest from O accelerates uniformly along a straight line andcrosses two points A and B which are 5 m apart in 2 s. If velocity at B is 2 m/s more than

the velocity at A, find the distance OA.

8. A thin test tube of negligible weight isfloating in water ( density of water 1gm/cm3)

with some liquid A filling part of its lengthto keep it upright. When the test tube is threefourths full it is just about to submerge asshown . When another liquid B fills half thelength of the tube, one fourth of the length ofthe test tube is seen above water. Find thedensity of the two liquids

9. A point object is located on the principal axis of a lens at a distance of 25 cm from it.When the object is moved 5 cm away from the lens the image moves by 40 cm. Find the

focal length of the lens

10. Two wires made of same material have their thicknesses in the ratio 1:2 and have equallengths. When connected in parallel, their equivalent resistance is R. Find the equivalent

resistance when they are connected in series.

11. A magnet is arranged parallel to an external uniform magnetic field of induction Bo withits north pole pointing in the direction of the field. At a point on the equatorial line of themagnet the magnetic induction is zero. Find the induction at double this distance on the

axial line of the magnet.

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12. Find the current in the diagonal resistance. All resistances are equal.

13. A straight conductor carries a current vertically upward. A charged particle movinghorizontally towards the wire is at an instant located to the east of the wire. Find the

direction of the magnetic field at the position of the charged particle and the direction ofthe force on it.

14. A longitudinal wave of frequency 1000 Hz is travelling in a medium at 350 m/s. At a

certain point in the medium there is a compression at a certain moment. How manymilliseconds later would the next rarefaction form at this place. How far is the earlier

compression at this time.

15. Fission of one uranium nucleus evolves 200 MeV of energy. Find the number of nucleiiof uranium that should undergo fission to evolve energy required to power a 40 W lamp

for 25 hrs. How many micrograms of mass has disappeared in the process.

PHYSICS - 2003

1. Two boats A and B can each travel at 4 m/s relative to a stream. At a certain moment they

are 1.2 km apart with A going down stream and B upstream. The stream is flowing at 2m/s. How far apart are they 20 s after they cross each other. If the engine of boat B wereto fail at the moment the boats cross and the boat B were to travel with the stream, find

the distance between the boats 30 s after the crossing.2. Two long trains are moving in opposite directions on parallel paths. One at 36 kmph and

the other at 72 kmph. A person sitting in the slower train sees the faster train taking 20 sto pass him. Find the length of the faster train. If an observer in the faster train sees the

slower train passing him in 10 s find the length of the slower train. How long do thetrains take to cross each other.

3. Reaction time of a driver is the time interval between the moment the driver sights an

obstacle and the moment he applies the brakes. During this time the car travels with aconstant speed at which he is driving and gets nearer to the obstacle.A driver has a reaction time of 0.5 s and is travelling at 72 kmph on a straight road. Whatshould be the minimum deceleration produced by the brakes of his car if he should avoid

hitting an obstacle 50 m away from the car at the moment he sees it.

4. A toy rocket leaves the ground with zero initial velocity and accelerates for 5 s at 2 m/s2.The fuel is finished at this moment and it continues to move up till its velocity becomeszero. Find the maximum height reached by it and the total time for which it is in the air

before returning to the ground.

5. A cylindrical vessel of base area 50 cm2

and height 25 cm is filled with one litre of water.A cube of side 5 cm made of a material of relative density 0.8, is lowered in to the vessel.By how much will the level of water rise. What part of the cube can be seen above water?

If the height of the vessel were 22 cm, how much water would have overflown?

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6. A point object is located as shown. Find thepoint of convergence or divergence of the raysthat pass through the lens.

Also find the point of convergence or divergence of the rays from the object after they pass through the lens,if the object is moved parallel to the principal axis and away from the lens by 10 cm. Focal length of the lensis 20 cm.

7. Graphs of sine of angle of incidence in medium 1(on the x axis) and sine of angle of refraction inmedium 2 ( on the y axis ) as ray of light travelsfrom medium 1 to 2 are as shown.

One of the graphs is for violet colour and the other is for red. What are the refractive indices for the red andviloet colours of medium 1 with respect to medium 2. One of the graphs is for violet colour and the other isfor red. What are the refractive indices for the red and viloet colours of medium 1 with respect to medium 2.

8. Two small spheres have their radii in the ratio 1:2 and are some distance apart. They havecharges of - 6 m C and 12 m C and exert a force of 12 N on each other. The spheres arenow connected by a conducting wire and the distance between them is halved Assume the

total charge on them is shared in the direct ratio of their radii after the connection andfind the new force between them.

9. A long conductor is carrying current towards north. A moving charged particle A locatedat a certain instant vertically above it has a velocity directed southward and the force on itis directed upward. What is the sign of the charge on A. Find the direction of the force onan oppositely charged particle B moving northward and located at a certain instant to the

east of the conductor.

10. Sections ACB and ADB of the wire shown have thicknesses inthe ratio 1:2 and are made of same material. A current of 7 Aenters at A. Find the currents in the sections ADB and ACB. Ifthe potential difference between A and B is 18 V, find theresistances of the wires ACB and ADB.

11. A satellite is revolving in a circular orbit in the equatorial plane and completes onerevolution in 90 min relative to the centre of the earth. What is the time interval betweenthe successive crossings of the satellite over a point on the equator if the satellite is

spinning from a) west to east b) east to west.

12. Find the energy in joules per reaction of the following nuclear reaction.

the masses of are 2.0141 u, 4.0026 u, 1.0078 u and 1.0087 u

respectively. A city consumes 1016J of energy per year. How many kg of sea water is needed peryear, if 0.015% of hydrogen atoms in sea water are deuterium.

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PHYSICS-2004

1. A car traveling at a certain speed v1 overtakes another car traveling at a slower speedv2 at A. An hour later the faster car reverses its direction, changes its speed to v 3 andafter some time meets the slower car now coming in the opposite direction atposition B. The distance between the positions A and B is 10 km. Find the speed ofthe slower car if v1 - v2 = v3 + v2. Find the value of v2.

2. Two lenses of focal lengths f1 and f2 kept in contact can be replaced by a single lensof focal length f. This focal length is given by the following formula

3. In using this formula the focal length of a convex lens is taken as positive and thefocal length of a concave lens is taken as negative. Use this formula to solve thefollowing problem.

A point object is placed 36 cm away from a convex lens and its image is formedon a screen placed 180 cm away from the lens on the other side. If now a secondlens is placed in contact with the first lens, the screen has to be shifted by 90 cmtowards the lenses in order to obtain a clear image on it. What is focal length of thesecond lens? The screen is fixed at this position now and the focal length of thesecond lens is doubled. Find the distance through which the object has to be shiftedto obtain a clear image on the screen.

4. Three conducting wires of equal radii having lengths in the ratio 1:2:3 have theirresistivities in the ratio 2:3:4. These wires are connected end to end. When a certainpotential difference is applied between the free ends of the combination, potentialdifference between the ends of middle conductor is found to be 60 V. Find thepotential differences between the ends of the other conductors. If the rate of heatproduction from the first conductor is 4 W, find the rate of heat production from theother two.

5. Two cubes made of same material have some hollow space in them and are floatingin a liquid of density 2 g/cm3. One cube is just floating while the other has threefourths of its volume below water. If the cavities in the cubes have their volumes inthe ratio 1:2 find the density of the material of the cube.

6. A long horizontal conductor carrying a current is oriented along east west line. Anelectron located above the conductor and moving eastward experiences a forcetowards the conductor. Another electron located vertically below the conductor hasits velocity directed towards the conductor. Find the direction of force on thiselectron.

6. A certain transparent slab exhibits aninteresting property. Its refractive indexhas two different values for a givenwavelength. A ray of light is passing fromthis medium in to air and is incident at a

certain angle at its interface with air. Therefracted ray 1 for which the refractiveindex with respect to air is 2 grazes thesurface of separation and the otheremerges in to air making an angle of 30with the first refracted ray. Find the anglebetween the incident and the secondrefracted ray

7. If two charged conducting spheres are connected by a wire charge flows from oneto the other till the charges on them are in the ratio of their radii. Two small

spheres having radii in the ratio 2:1 have charges of2Q and Q on them and aresufficiently far apart to be treated as point charges. They exert force of F on each

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other. A conducting wire now connects them. Find the force between them afterthe charges get redistributed on them.

8. All resistances shown in thefigure are equal. Equivalentresistance between A and B whenresistance between C and D isremoved is R. The removedresistance is reconnected and theresistances between the cornersB,C and D,E are now removed.What is the equivalent resistancebetween A and B now.

9. A horizontal force of 10 N acts on a block of mass 5 kg lying on a smoothhorizontal surface. The block is initially at rest. This force stops acting after 5 sand the body continues to move. 5 s later a force of 20 N starts acting againstthe motion of the block till the block stops. What is total distance covered bythe block.

10. Two cubes made of same material are placed alongside. When a temperaturedifference of 100 C is maintained between their farther faces, heat is found tobe conducted at a rate R through them. The cubes are now placed one above theother. If the same temperature difference is maintained between the bottom andtop faces find the new rate of heat flow. Also find the temperature differencebetween the bottom and top faces for the rate of heat flow to be R again. (Heatflow is analogous to current flow).

11. A hollow tube is 68 m long. When struck at one end an observer at the otherend receives two notes, one due to sound traveling in air and the other throughthe metal. Estimate the time interval between receiving the sound notes. (Speedof sound in air = 340 m/s, Youngs modulus of the material of the tube= 2 1011 N/m2 and density of the material = 8 g/cm3).

12. About 0.2 amu of mass disappears in the fission of a single uraniumnucleus (mass number 235). Find the energy released in the fission of 4.7 g ofuranium. Express this energy in joule.

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