Gravitation Questions and Answers

te is moving around the earth with speed V in circular orbit of radius r If the orbital radius is decreased by 2 the speed of the satellite will 2 Increase by 0 5 1 Increase by 1 3 Decrease by 1 4 Decrease by 0 5 The pressure of water in a water pipe w

In one waterfall the water falls 300m Calculate the decrease in the gravitational potential energy g p e of 1 0kg of water as it falls through this distance decrease in g p e 2 iii Assume that the increase in internal energy of the 1 0kg of water is equal to its decrease in g p e Calculate the rise in temperature of the water The specific heat capacity of water is 4200 J kg C

27 If G is the universal gravitational constant and the uniform density of a spherical planet Then shortest possible period of rotation around a planet can be p is a TG 2p b 3TG V p P c T 6 Gp d 3r VGp

38 If radius of a solid sphere is decreased to half keeping density of sphere unchanged the slope of E r graph inside the sphere will a remain unchanged b become two times c become four times 1 d remain th 8

7 Two point masses each of mass M are kept fixed at rest at points A and B respectively A third m is released from infinity with a negligible speed so that it can move along y axis under the influence of mutual gravitational attraction on it due to point masses kept at A and B respectively as shown in the figure 1 Figure 2 represents the potential energy of system incudes m M at A and M at B with position of m at y axis Neglect any other forces other than gravity given Gm d 12 Joule m 6 kg Choose the correct option s m 2m

24 The diagram shows a barrel of weight 1 0 10 N on a frictionless slope inclined at 30 to the horizontal Force of slope on barrel Slope Force a 2 5 10 J c 5 0 x 10 J Barrel 1 0 10 N 30 The force is parallel to the slope What is the work done in moving the barrel a distance of 5 0 m up the slope b 4 3 10 J d 1 0 10 J COMEDI

Consider two solid spherical asteroid of uniform density of mass M and radius R In one asteroid a tunnel of very small size of depth R is bored to the centre and in other asteroid a spherical cavity of radius R 2 is made as shown in the figure Now identical particles of mass m dropped into the cavities of both asteroids from the top most point P If force experienced by particle is F and F respectively in cavities of asteroids I and II when they are x distance away from the centre of asteroids If the time taken by particles to reach the centre of asteroids is T and T respectively then A The ratio of F F is equal to 2x R B The ratio of F F is equal to x R D The ratio of T T is equal to 1 2 C The ratio of T T is equal to t 4 Asteroid I Asteroid 111 M R uneita fuciu fara affe qui fe R 2 from east R farger et af d x fave I a II at find and FT T 1 A F F ww B ar F F D T T

3 In space two point masses of mass 10 kg each are fixed The masses are separated by a distance 10 m Another point mass of mass 1 kg is to be projected from the point at midpoint of line joining the fixed masses such that it escapes to infinity The minimum speed of the projection is 1 G m s ac mla 21 2 2G m s LA

th options without selecting any incorrect option second option in this case will result in 2 marks Selecting only one of the three correct options either first or third or fourth option without selecting a marks Selecting any incorrect option s second option in this case with or without selection of any correct option s will result in 2 marks wo point objects of masses m and 4m are at rest at an infinite separation They move towards each other under mutual gravitational attraction If G is the universal gravitational constant then at a separation the total mechanical energy of the two objects is zero their relative velocity is 10Gm r the total kinetic energy of the objects is their relative velocity is zero 4Gm T

A plumb bob of mass 2 kg is hung from the ceiling of a car If the car moves with an acceleration ao up the plane and the angle of incline is 30 Find the tension in the string g 10 ms 2 aid ych dla ch crachl PR Sfaald Elld g 10 ms A 10 2 N B 10 3 N C 10 5 N AND FRUI a zsi 31 412 Gad 30 3 C 10 N FORUT

If the elevator in the shown figure is moving upwards with constant acceleration 1 m s the tension in the string connected to block A of mass 6 kg would be g 10 m s 1m s A 60 N 66 N 54 N 42 N

A balloon is ascending vertically with an acceleration of 0 2m s Two stones are dropped from it at an interval of 2 sec The distance in m between them 1 5 sec after the second stone is released is

2 The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M to transfer it from a circular orbit of radius R to another of radius R R R is 1 GmM 1 1 R R2 3 2GmM 1 R R GmM 12 yes 4 GmM 2 1 R R 1 1 R R

If one wants to remove all the mass of the earth to infinity in order to break it up completely The amount of energy that needs to be supplied will be x GM R where x is Round off to the Nearest Integer M is the mass of earth R is the radius of earth G is the gravitational constant

A bob of mass 2m hangs by a string attached to the block of mass m of a spring block system The whole arrangement is in a state of equilibrium The bob of mass 2m is pulled down slowly by a distance x and released A For x 3mg k Feeeeee C Frequency of oscillation of system is k 2m maximum tension in string is 4mg m B For x minimum tension in string is mg 3mg k 1 k 2 3m for all non zero values of x D The motion will remain simple harmonic for x 3mg

8 An object weighs 60 N on Earth a Determine the mass of the object b Determine the weight of the object in pounds c Determine the weight of the object in Newtons on the moon Recall g moon 1 6 g earth

A bob B of mass 1 kg is suspended from the ceiling and the side of a toy train as shown in the figure The train oscillates simple harmonically in horizontal direction with angular frequency w 5 rad s and amplitude a 0 1 m What is the ratio of maximum and minimum tensions in the string AB during the motion 2 g 10 ms tan 37 3 4 A L B Choose only 1 answer A 2 37 B 3 Your Answer

If R is the average radius of earth w is its angular velocity about its axis and g is the gravitational acceleration on the surface of earth then the cube of the radius of orbit of a geostationary satellite will be equal to Question Type Single Correct Type 1 2 3 R g R g Rg

A 494 kg uniform solid sphere has a radius of 0 392 m Find the magnitude of the gravitational force exerted by the sphere on a 50 1 g particle located a 1 58 m from the center of the sphere N b at the surface of the sphere N c 0 196 m from the center of the sphere N

Q14 If a person with a spring balance and a body hanging from it goes up and up in an aeroplane the reading of the weight of the body as indicated by the spring balance will AllMS 1998 JIPMER 20001 a Go on increasing b Go on decreasing c First increase and then decrease d Remain the same

A satellite of mass m initially at rest on the surface of earth is launched into a circular orbit at a height equal to the radius of the earth The minimum energy required is Question Type Single Correct Type 13mgR 1 2 mgR 1 3 mgR

Three equal masses m placed at the corners of a equilateral triangle of side a then find net gravitational force on any one mass m O Gm a2 O Gm O Gm 3a V3 Gm2 a me 60 m h

If a particle of mass m is released from a height 3R above earth s surface then its kinetic energy when its reaches on earth s surface M is mass of earth and R is its radius Question Type Single Correct Type 1 2 3 1 GMm 4 R 3 GMm 4 R GMm

53 sphere of uniform density and 4 m Its centre is at the origin of the coordinate system Two spheres of radii 1 m are taken out so that their centres are at P 0 2 0 and Q 0 2 0 respectively This leaves two spherical cavities what is the gravitational potential at any point on the circle x 6 GM X GM

The density of a nearly discovered planet is twice that of the earth The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth If the radius of earth is R the radius of the planet would be Question Type Single Correct Type 1 2R 2 4R 3 R 4 4 R 2

51 A solid sphere of uniform density and mass M has radius 4 m Its centre is at the origin of the coordinate system Two spheres of radii 1 m are taken out so that their centres are at P 0 2 0 and Q 0 2 0 respectively This leaves two spherical cavities What is the gravitational field at the origin of the coordinate axes 1 31GM 1024 3 31GM 52 In problem 51 what is the gravitational field at the centre of the cavities 31GM 1 1024 1 2 Gm 1024 4 Zero GM Gm 1024 3 31GM 53 In problem 51 what is the gravitational potential at any point on the circle x 6 2 2 4 GM GM 64 10 CH

A body attains a height equal to the radius of the earth when projected from earth surface The velocity of the body with which it was projected is Question Type Single Correct Type 1 2 GM VR 2GM R

Figure shows variation of acceleration due to gravity with distance from centre of a uniform spherical planet Radius of planet is R What is r 1 g 1 2 R 4 go Question Type Single Correct Type 7R 4 g 4 r r r

Q 30 Assuming that the moon describes a circular orbit of radius R about the earth in 27 days and that Titan describes a circular orbit of radius 3 2 R about Saturn in 16 days compare the mass of Saturn and the earth a 25 2 1 b 46 4 1

19 A massive particle of twice the mass of earth is dropped from a height h above earth s surface Fin the distance moved by the particle before strikin earth 1 3 flm 2h 2 2h 3 4 almost h

sives A 11 At point X shown above which is midway between the centers of two isolated planets of radii R and 2R the net gravitational force on an object is zero If the mass of the smaller planet is M the mass of the larger planet is M 4 M 2 C M D 2M B R E 4M X 2R

m or 10 HR ves A B 27 Planet X has a mass M radius R and no atmosphere An object of mass m is located a distance 2R above the surface of planet X as shown in the figure above The object is released from rest and falls to the surface of the planet What is the speed of the object just before it reaches the surface of planet X Jests on D 2GM 3 R 4GM 3R 8GM M 3GM R R Planet X

0 The time period of an artificial satellite in a circular orbit of radius Ris 2 days and its orbital velocity is vo If time period of another satellite in a circular orbit is 16 days then a its radius of orbit is 4R and orbital velocity is vo b its radius of orbit is 4 R and orbital velocity is Vo 2 c its radius of orbit is 2R and orbital velocity is vo d its radius of orbit is 2R and orbital velocity is Vo 2

39 In the figure a spherical ball of radius R 2 has bee radius R A small uniform spherical body of mass removed from a uniform sphere of mass M and 2M is placed at a distance of 2R from the centre of the spherical cavity as shown in the figure The magnitude of the gravitational intensity at the centre of the cavity is a zero R Georgheghchachafen GM b 28 O R 2 c 2M 2 GM R d GM 28

5 A ring has a total mass M but non uniformly distributed over its circumference The radius of the ring is R A point mass m is placed at the centre of the ring Work done in taking away this point mass from centre to infinity is 2GmM GMm b R R a GMm c 2R d 3GMm 2R

37 Gravitational force between two charged and electrostatic force between them is F2 They are at distance r from each other Now the air between them is sucked out and distance is increased to 2r Then the new forces F and F2 are such that F a F F F 4 4 c both are correct d both are wrong b F2

7 Imagine earth to be a solid sphere of mass M and radius R If the value of acceleration due to gravity at a depth d below earth s surface is same as its value at a height h above its surface and equal to where g is the value of acceleration due to 4 h gravity on the surface of earth the ratio of will be d 2017 Gujarat a 1 b 3 C 3 2 d 2 wir 3

A narrow tunnel is dug inside the earth along one of its diameters Radius of earth is R 2GM and its mass is M A particle is projected inside the tunnel with velocity from one of its ends then maximum velocity attained by the particle in the subsequent motion is nGM assuming tunnel to be frictionless Find n 4R VR

44 A spherical planet has uniform mass density p A satellite is orbiting around it in circular path The minimum time period of the satellite is 3 d VGp a T V Gp b 2 Gp c 2 Gp

R 38 A spherical hole of radius is made in a solid sphere 2 of radius R The mass of the sphere before hollowing was M The gravitational field at the centre of the hole due to remaining mass is a zero GM 2R2 c GM 8R 2 GM R b d Sis

41 A planet of density p is rotating with time period T about its own axis Find the smallest possible time of revolution of the planet such that a particle does not leave contact with the planet on the 3r 4 106 SI units equator PG a 2000 s c 3000 s b 1000 s d 4000 s

A fixed sphere of radius R and uniform mass density d has a cavity of radius R 2 as shown in figure The centre of the solid sphere was at C while that of the cavity is O A liquid of density d 2 is filled in the cavity Find the gravitational force exerted by the liquid on solid sphere Gx R d RY Gn R d Gx R d D G R d 0

A ball is thrown upwards from a planet such that distance travelled in the 4th or 5th second is one forth of the distance travelled in the first two seconds of its downward journey If the maximum height attained by the ball is 32m choose the correct statement s Question Type Multiple Correct Type 1 Acceleration due to gravity of the planet is 2 m s 2 Acceleration due to gravity of the planet is 4 m s 3 4 Distance travelled by the ball in 4th second is 2m Time taken for the ball to strike ground again is 10 s

10 A circular ring of mass M and radius a is placed in a gravity free space A small particle of mass m placed on the axis of the ring at a distance 3a from the centre of the ring is released from rest The velocity with which the particle passes through the centre of the ring is GM a a GM M c 1 26 m b d GM m 2a M GM M

ook at your proportionality relation for the escape speed Describe two ways you could increase the escape speed of a lanet to be faster than the speed of light by changing only one variable at a time

The earth s radius is R and acceleration due to gravity at its surface is g If a body of mass m is sent R from the earth s surface the to a height of 4 potential energy increases by A B C D mg R 3 R mg 4 R mg 5 R 3mg 16

mum height attained by the ball after second collision iii e 0 5 g 10 m s A ball is thrown vertically upward from ground with speed 40 m s It collides with ground after returning Find the total distance travelled and time taken during its bouncing e 0 5 g 10 m s orizontal plane and rebounds If e 0 2 is the coefficient of C

A spherical hole is made in a solid sphere of radius R The mass of the sphere before hollowing was M The gravitational field at the centre of the hole due to the remaining mass is A Zero R 2

The mass of a planet is six times that of the earth The radius of the planet is twice that of the earth If the escape velocity from the earth is then the escape velocity from the planet is O 3v O 2v

Q 18 MODERATE 4 1 01 31 O If the earth rotates faster than its present speed the weight of an object will Increase at the equator but remain unchanged at the poles Decrease at the equator but remain unchanged at the poles Remain unchanged at the equator but decrease at the poles