Gravitation Questions and Answers

1 Increase by 225 3 Increase by 125 2 Decrease by 56 4 Decrease by 144 If G is universal gravitation constant and g is acceleration due to gravity then dimensions of 1 M L 3 ML 2 M L 4 M L 69 will be

5 If radius of earth contracted by 0 1 its mass remaining same then weight of the body at earth s surface will increase by 1 0 1 3 0 3 2 0 2 4 Remains same

18 Two concentric shells of masses M R and M are concentric as shown in the figure Which of the following is correct regarding the gravitational force on m due to M and M at points P Q and R a Fp 0 b Fo c FR G M M 2 Q a b GM m b d All are correct P M d at

49 Four equal masses each of mass M are placed at the corners of a square of side a The escape velocity of body from the centre O of the square is 8 2GM a 4 c 2GM 4GM a a b d a 4 2GM a

50 Energy of a satellite in circular orbit is Eo The energy required to move the satellite to a circular orbit of 3 times the radius of the initial orbit is Eo 3 d E a Eo 3 b 2E0 GMM

The minimum and maximum distances of a satellite from the centre of earth are 2R and 4R where R is radius of earth If mass of the earth is M the maximum speed of satellite will be 2 1 3 GM VR 3GM V 2R 4 GM 2R 2GM 3R

2x 5 body of 47 What impulse need to be given to a tunnel passsing through centre of earth at the c released from the surface of earth along a straight of earth to bring it to rest Mass of earth M radius of earth R a m VR b GMm c m d GM V2R VR shells of masses M d Zero R 6

orbit 5 If an artificial satellite is moving in a circular around the earth with a speed equal to half the height of the satellite above the surface of the earth is magnitude of the escape velocity from the earth the R R a 2 R 2 d 4 f 1 kg infinity to an

5 If R is the radius of the earth and g the acceleration due to gravity on the earth s surface the mean density of the earth is A 4 G 3gR B 3TR 4gG C 3g 4TRG D Rg 12G

7 Suppose a smooth tunnel is dug along a straight line joining two points on the surface of the earth and a particle is dropped from rest at its one end Assume that mass of earth is uniformly distributed over its volume Then a the particle will emerge from the other end with velocity GM V 2R respectively 9 where M and R are earth s mass and radius e b the overlapping will come to rest at centre of the tunnel c potential energy of the particle will be equal to zero at centre of tunnel if it is along a diameter d acceleration of the particle will be proportional to its distance from mid point of the tunnel ing in a circular orbit round the certain noin

a 6 31 A particle would take a time t to move down a straight tube from the surface of earth supposed to homogeneous sphere to its centre If gravity were to remain constant then the time would be t The ratio of t t will be be a T a 2 2 b c 2 d TU 4 E L to T 2 2 th satellite of mass m revolves in a circular

Two particles of equal masses are revolving in horizontal circular paths of radii r and r2 respectively with the same time period The ratio of their centripetal force is Question Type Single Correct Type 1 2 2

If the earth rotates faster than its present speed the weight of an object will Question Type Single Correct Type 1 2 3 A 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 Remain unchanged at the equator but

A small satellite is in elliptical orbit around Earth as shown If L denotes the magnitude of its angular momentum and K denotes kinetic energy L L and K K L L and K K L L and K K Earth

A black hole is an object whose gravitational field is so strong that even light cannot escape from it To what approximate radius would earth mass 5 98x1024 kg have to be compressed to be a black hole 1 10 m 2 106 m 3 10 2 m 4 100m 24M

Energy required to move an Earth s satellite of mass m from an orbit c radius R to 5R is M mass of earth R radius of earth Options GMm 5R 2GMm 3R 2GMm

A tunnel is dug across the earth of mass M and radius R at a distance R 2 from the centre O of the Earth as shown A body is released from rest from one end of the smooth tunnel The velocity acquired by the body when it reaches the centre C of the tunnel is A 3GM 2R 3GM 8R B D 3GM 4R 3GM 16R C R 2 R

3 10 km s 4 11 2 KM S 3 The ratio of kinetic energy required to be given to the satellite to escape from earth s surface to the kinetic energy required to be given to the same satellite to revolve round the earth in an orbit just above earth s surface is 1 1 1 3 2 1 2 2 1 4 4 1 und garth in a circular orbit at a uniform speed v If gravitational force suddenly

4 4 15 A satellite of mass 200 kg revolves around a planet of mass 5 x 1030 kg in a circular orbit of radius 6 6 x 105 m Binding energy of the satellite is 1 5 x 1015 J 3 1016 J 16 5 x 1015 J 2 4 1016 J Two satellites A and B go round the planet P in circular orbits having radii 4R and R respectively If the speed

9 A satellite is revolving around earth in a circular orbit at a uniform speed v If gravitational force suddenly disappears speed of the satellite will be 1 Zero 3 2v D Mark the correct statement 2 V 4 Infinity

Mark the correct statement Escape velocity does not depend on mass of body ii If total energy of a satellite becomes positive it escapes from earth Orbit of geostationary orbit is called parking orbit iii 1 i only 3 i ii and iii 2 i ii only 4 i iii only

3 4 4 9 10 Weight of a body decreases by 1 5 when it is raised to a height h above the surface of earth Whe same body is taken to same depth h in a mine its weight will show 1 0 75 increase 3 0 decrease 2 4 1 5 decrease 3 0 75 decrease

If mass of earth decreases by 25 and its radius increases by 50 then acceleration due to gravity at surface decreases by nearly 1 89 3 33 2 67 4 11

8 Two point objects of mass 2x and 3x are separated by a distance r Keeping the distance fixed how mu mass should be transferred from 3x to 2x so that gravitational force between them becomes maximum 1 3 x 4 X X 2 2 4 X 3 2x 3

A satellite is moving in a low nearly circular orbit around the earth Its radius is roughly equal to that of the earth s radius Re By firing rockets attached to it its speed is instantaneously increased in the direction of its motion so that it become A 2Re C 4Re 3 122 larger Due to this the farthest distance from the centre of the earth that the satellite reaches is R Value of R is B 3Re D 2 5Re times

9 At what depth from earth surface the acceleration due to gravity is changed by 5 geat at de fondai Teus 4 yaralu aku 5 Rafa Gr m 2 640 km 3 320 km 1 64 km 4 32 km 0 A negative charge is coming towards the observer The direction of the magnetic field produced by it will be as seen by observer S304 giacha fa I al 3ch RI v G T

A body is moving in a low circu about a planet of mass M and ra The radius of the orbit can be taken itself Then the ratio of the speec body in the orbit to the escape from the planet is A 2 C 2 B 1 D 5

5 15 The acceleration due to earth s gravity on a point particle at a height h above the surface of the earth is denoted by g h and at a depth d below the surface of the earth is denoted by g d Consider the earth to be a sphere of radius R with uniform mass density Which of the following correctly represents the ratio g d g d X 1 X 2 3 4 p b p 6 p 6 p 6 p 6 p 6 1 00 0 75 0 50 0 25 0 00 0 00 1 25 1 00 0 75 0 50 0 25 p 6 p 6 1 25 1 00 0 75 0 00 0 00 0 25 0 50 0 75 1 00 d R 0 50 0 25 0 00 0 00 1 25 1 00 0 75 0 50 0 25 0 25 0 00 0 50 0 75 1 00 1 25 d R 0 25 0 50 0 75 1 00 d R 0 00 0 25 0 50 d R 0 75 1 00

4 ms 28 If gravitational attraction between two points masses be given by F G satellite in a circular orbit will be proportional to b r a r mm2 Then the period of a pr 1 c r d independent of n 29 Suppose the gravitational force varies inversely as

4 A planet of mass m moves around the sun of mass M in an elliptical orbit The maximum and minimum distance of the planet from the sun are and respectively The time period of the planet is proportional to a 7 2 c 1 1 2 b r 2 d r 3 2 1 C the surface of the

19 Compute the additional velocity required by a sa orbiting around earth with radius 2R to become from earth s gravitational field Mass of earth is M 2 1 a c 2GM 2 1 VR GM 3 1 VR b d GM 2R GM R 2 1 27 As W es 2M m and M are respectively

A particle is projected from point A that is at a distance 4R from the centre of the earth with speed v in a direction making 30 with the line joining the centre of the earth and point A as shown The particle passes grazing the surface of the earth Consider gravitational interaction only between these two Find v in km sec GM use 6 4x107m s R THE NAR 4R D R A GROUP

A 200 kg satellite is revolving around earth in circular orbit of radius 2R Amount of energy required to transfer it to a circular orbit of radius 4R is M 6 1024 kg R 6 4 106 m O 1 57 10 J 1 57 x 106 J 3 13 x 10 J 12 106 1

Two bodies each of mass mare initially at rest at infinite distance apart Now they move towards each other under gravitational force The relative velocity of approach at a separation d between them is 1 2Gm d 3 C 2 4 4Gm d 2G m

if I have two masses of m1 and m2 in vaccu m and the only force between both the mas ses is of the gravitational force how much t ime would it take for both masses to touch each other due to gravitational attraction h ow do we analysie the motion of both objec ts

Assume that we don t neglect the angle between the axis of rotation and perpendicular to the orbit As venus moves to the diametrically opposite point in it s orbit the axis of the rotation is will be tilted in which manner A C O Sun O Sun B D OSun O Sun O Sun

A radar has a power of 1 kW and is operating at a frequency of 10 GHz It is located on a mountain top of height 500 m The maximum distance in km upto which it can detect ob ject located on the surface of the earth Radius of earth 6 4 106 m is

Q8 A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km Then the time period of a spy satellite orbiting a few hundred kilo meters above the earth surface Re 6400 km will 2002 approximately be A h B 1h C 2 h D 4h

Calculate the self gravitational potential energy of matter forming a a thin uniform shell of mass M and radius R and b a uniform sphere of mass M and radius R 1 In a certain region of space gravitational field is given by I K r Taking the reference point to be with V V find the potential as a function of distance r

33 From the top of a tower T a ball is thrown vertically upwards When the ball reaches h below T its speed is double of what it was at a higher h above T Show that the greatest height attained by the ball above T is 5 h 3 Ans 5 h

Orbit Speed Kepler s Second Law Set your planet at x y 100 0 as before and choose a y velocity 30 35 units la velocity Describe the speed of the planet as it moves around the orbit Where is the pl When is it moving slowest Circular motion velocity of the planet

6 53 A body is projected vertically upwards from the surface of earth with a velocity sufficient to carry it to infinity Calculate the time taken by it to reach height h 3 2 2R ARE 1 4 1 Ans 1 3 g R

6 58 Two satellites move in circular orbits around the earth at distances 9000 km and 9010 km from earth s centre If the satellite which is moving faster has a period of revolution 90 minutes Find the difference in their revolution periods Ans 9 s

Q 29 A large spherical mass M is fixed at one posi tion and two identical point masses m are kept on a line passing through the centre of M see figure The point masses are connected by a rigid massless rod of length and this assembly is free to move along the line connecting them All three masses interact only through their mutual gravitational interaction When the point mass nearer to M is at a distance r 31 from M the tension in the rod is zero for m k The value of k is 2015 288 7

riginal orbit The sea level and at top of mountains are w W2 and w3 respectively then b W W W3 dat wy W W3 d w W W3 c w W W3 hody is projected from earth s surface to become qolution will not

10 In an am 0 2 of main current pass through the galvanometer If resistance galvanometer is G the resistance of ammet will be a c 1 499 G 1 G 500 b d 499 G 500 500 499 G

Two identical satellites are at the heights R and 7R from the Earth s surface Then which of the following statement is incorrect r radius of the Earth 1 Ratio of total energy of both is 5 2 Ratio of kinetic energy of both is 4 3 Ratio of potential energy of both 4 4 Ratio of total energy of both is 4 and ratio of magnitude of potential to kinetic energy is 2

A space telescope in orbita around the Earth discovers a new planet which is observed to move around the Sun by an angle of 4 72 milliradians in a year Assuming a circular orbit estimate the distance in A U of the planet from the Sun 121

Two spherical bodies of mass M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R If they attract each other due to gravitational force only then the distance coyered by the smaller body before collision is a 117 5R c 2 5R 6 1 5R d 4 5R 2015 11 71

6 64 Two satellites S and S revolve around a planet in coplanar circular orbits in the opposite sense The periods of revolutions are T and nT respectively Find the angular speed of S as observed by an astronaut in S when they are closest to each other Ans 2 3 2 n 1 T n 3 1