Gravitation Questions and Answers

D The distance between the centres of the earth and the moon is 60 times the radius of the earth Calculate the centripetal acceleration of the moon Acceleration due to gravity on the earth s surface 10 ms

01 The acceleration due to gravity at height R above the surface of the earth is g 4 The periodic time of a simple pendulum in an artificial satellite at this height will be 1 T 2 21 g 2 T 2n 1 2g 3 Zero 4 Infinity

A solid sphere of uniform density and radius 4m is located with its centre at the origin O of coordinate system Two spheres of equal radius 1m with their centres at A 2m 0 0 and B 2m 0 0 are taken out of the solid sphere leaving behind spherical cavities as shown in the figure Then gravitational potential at the centre of the sphere is Vo GX volts Fill X in your answer sheet Given G 10 1 Nm kg 20 3

The gravitational force of attraction between a uniform sphere of mass M and a uniform rod of length and mass m as shown in figure is GMm a r r l c Mmr M 1 111 b GM 2 d 1mM

18 A satellite is describing a circular orbit around a massive planet of radius R The altitude of the satellite above surface of planet is 3R and its speed Vo To place the satellite in an elliptical orbit which will bring it closer to the planet its velocity is reduced from Vo to BV when B 1 The find K smallest permissible value of if satellite is not to crash on the surface of planet is

A satellite is launched into circular orbit of radius Raround the earth while a second satellite is launched into an orbit of Radius 1 02R The percentage change in the time periods of the two satellite is 1 0 7 2 1 0 3 1 5 4 3

7 Two solenoids acting as short bar magnets P and Q are arranged such that their centres are on the X axis and are separated by a large distance The magnetic axes of P and Q are along X and Y axes respectively At a point R midway between their centres if B is the magnitude of induction due to Q then the magnitude of total induction at R due to the both magnets is Hhail a 3B b 5B 5 2 B d B

9 At what depth below the surface of the earth the acceleration due to gravity will be i one half ii one fourth of the acceleration due to gravity at the surface of the earth Radius of the earth is 6400 km Ans i 3200 km ii 4800 km

An object of mass M is divided into two parts which are placed at distance d If gravitational force of attraction is maximum between parts then find the ratio of mass of both parts

2 1 a Write the answers of the following questions 1 Complete the following block m1 m2 m1

A geo eostationary satellite is orbiting the earth at a height of 5R above that surface of the earth R being the radius of the earth The time period of another satellite in hours at a height of 2R from the surface of the earth is

9 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 12 R If they attract each other due to gravitational force only then the distance covered by the smaller body before collision is AIPMT 2015 1 1 5R 3 4 5R 2 2 5R 4 7 5R

Two small balls of mass m each are suspended side by side by two equal threads of length L as shown in the figure If the distance between the upper ends of the threads be a the angle 0 that the threads will make with the vertical due to attraction between the balls is E 3 tan 0 1 tan 1 a X g mG 1 a x g mG a a x 0 L E 2 tan 4 tan mG a x g a x g

Two bodies with masses M and M are initially at rest and a distance R apart Then they move directly towards one another under the influence of their mutual gravitational attraction What is the ratio of the distances travelled by M to the distance travellel by M 1 M M 3 1 2 4 M M C 1

5 The SI unit of electric field is 6 a newton coulomb b Volt meter The electric field required to c coulomb newton d both a and b

4 A 1500 kg satellite orbits the moon at an altitude of 2 3 10 m What is the period of the satellite R 174x10 m r 2 3x10 m moon R 1 74 x 10 m

If M is the mass of earth and M is the mass of e m e moon M 81 M The potential energy of an object of mass m situated at a distance R from the centre of earth and r from the centre of moon will be 1 GmM m 3 GmMm R r 81 81 1 R r 1 R 2 GmM 4 GmMm e 81 1 R 1 r 81 1 R

Three point masses each of mass m rotate in a circle of radius r with constant angular velocity due to their mutual gravitational attraction If at any instant the masses are on the vertices of an equilateral triangle of side a then the value of oo is Gm 1 2 3Gm 3 Gm 30 4 zero

20 At what height from the surface of earth the gravitation potential and the value of g are 5 4 x 107 J kg and 6 0 m s respectively Take the radius of earth as 6400 km

Two satellites of earth S and S are moving in the same orbit The mass of S is four times the mass of S Which one of the following statements is true AIPMT Prelims 2007 1 The potential energies of earth and satellite in the two cases are equal 2 S and S are moving with the same speed 3 The kinetic energies of the two satellites are equal 4 The time period of S is four times that of S

1 The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth Then NEET 201

The height at which the weight of a body becomes 1 16th its weight on the surface of earth radius R is 1 3R 3 5R 2 4R 4 15R

The escape velocity for a planet is v A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface When the body reaches the centre of the planet its speed will be A v B 2 C D zero

Two identical solid uniform spheres each of radius R are kept touching each other Find how gravitational force of attraction between them depends on R 1 Far 1 3 Fa 1 a7 7 2 2 Fa 4 Far

c 40 hours Two spherical bodies of mass M and 5M radii R 2R respectively are released in free space with initial separation between their centres equal to 12 R If they attract each other due to gravitational force only then the distance covered by the smaller body just before collision is 2003 a 2 5 R c 7 5 R 4 5 R 1 5R b d

As seen in figure two spheres of mass m and a third sphere of mass M form an equilateral triangle and a fourth sphere of mass m is at the center of the triangle The net gravitational force on that central sphere from the three other spheres is zero a What is M in terms of m b If we double the value of m what then is th magnitude of the net gravitational force on the al cobara M

A space vehicle approaching a planet has a speed v when it is very far from the planet At that moment tangent of its trajectory would miss the centre of the planet by distance R If the planet has mass M and radius r what is the smallest value of R in order that the resulting orbit of the space vehicle will just miss the surface of the planet 1 v 3 R 10 2GM 2 r r 22GM 2GM r 2 Vr 1 4 R 2GMv

3 To measure the mass of a planet with the same radius as earth an astronaut drops an object from rest relative to the planet from an altitude of one radius above the surface When the object hits its speed is 4 times what it would be if the same experiment were carried out for Earth The ratio of mass of planet to the mass of earth is 1 2 2 4 3 8 4 16

A projectile is fired vertically upwards from the surface the earth with a velocity Kve where ve is the escape velocity and k 1 If R is the radius of the earth the maximum height to which it will rise measured from the centre of the earth will be neglect air resistance 1 1 k R 3 R 1 k 2 4 R 1 k R 12

e particles each of mass m are situated at the vertices of an equilateral triangle of side a The only forces acting on the particles are their mutual gravitational force It is desired that each particle moves in a circle while maintaining their original separation a The initial velocity that should be given to each particle and time period of circular motion are respectively 3GM a 2 a 3GM 2 GM 1 3GM V a 2x V a

In earth sun system if sun starts to shrink then force on earth due to sun Assuming that mass of sun is constant 1 Decreases 2 Increases 3 Remains same 4 First decreases then increases V pemain wurst accelera 1 ho 3 P Pa R R LLL

A spaceship is stationed on Mars How much energy must be expended on the spaceship to launch it out of the solar system Mass of the spaceship 1000 kg mass of the sun 2 1030 kg mass of Mars 6 4 1023 kg radius of Mars 3395 km radius of the orbit of Mars 2 28 x 108 km G 6 67 x 10 11 N m kg 2 NCERT 3 x 1011 J

7 If the law of gravitation becomes an inverse cube law instead of being inverse square law then 1 Planets will continue to move in elliptical orbits bona to noitentnaondo 2 The motion of a stone thrown by a person on the surface of the earth will be approximately parabolic 3 There will be no gravitational force inside a spherical shell of uniform density 4 Both 2 and 3

Work done to bring 4 particles each having a mass of 0 1kg from infinity to the vertices of square of side 0 2m is B 1 8 x 10 1 J 8 1 x 10 J B

13 India s Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the Sun It leaves the Earth at E and meets Mars at M If the semi major axis of Earth s orbit is a 1 5 x 10 1 m that of Mar s orbit 1 42 28 x 10 m taken Kepler s laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to a 260 days c 500 days M aM Mars orbit Sun GE Earth s orbit Mar s orbit E b 320 days d 220 days

P1 and The planets with radii R and R have densities P2 respectively Their atomospheric pressures are p and p2 respectively Therefore the ratio of masses of their atmospheres neglecting variation of g within the limits of atmosphere is 1 3 P R P P R P P R P 2 4 P R P2 P R P p R P P R P

A small satellite revolves around a heavy planet in a circular orbit At certain point in its orbit a sharp impulse acts on it and instantaneously increases its kinetic energy to k 2 times without change in its direction of motion Show that in its subsequent motion the ratio of its maximum and minimum distances k from the planet is assuming the mass of the satellite is negligibly small as compared to that of the 2 k planet 1

A skylab of mass m kg is first lauched from the surface of the earth in a circular orbit of radius 2R from the centre of the earth and then it is shifted from this circular orbit to another circular orbit of radius 3R The minimum energy required to place the lab in the first orbit and to shift the lab from first orbit to the second orbit are 3 1 mgr mgR 6 3 maR maR 2 mgR 3 4 mgR 12 4 2mgR mgR

A solid sphere of uniform density and mass M has radius 4 m Its centre is at the origin of the uib 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 31GM a 1024 Gm b 1024 d zero X 42 Z Fig 6 41

The density of a solid sphere of r 2 R center If the gravitational field due to this sphere at a distance 4 R from its center is E and G is the gravitational constant the ratio E GR p r 20 a is 5 where r is the distance from is b 3T c 3 T 2 d TS EAMCET 17 Lore

5 Suppose earth is a solid sphere of radius R made of a material of density P There is a spherical cavity inside earth whose centre is at B Distance of centre B from the centre of earth A is a A particle is projected from point D with a velocity u towards the centre of the cavity with a velocity u and the particle strikes the surface of cavity at point C as shown in figure Then 1 U 2 G R 3 A C B 1 2 U G R 3

Q11 A geostationary satellite is at a height h above the surface of earth If earth radius is R R A The minimum colatitude on earth upto which the satellite can be used for communication is sin R R h B The maximum latitudes on earth upto which the satellite can be used for communication is cos R R h C The area on earth escaped from this satellite is given as 2xR 1 sine D The area on earth escaped from this satellite is given as 2nR 1 cos0

The ratio of the mass of the moon to that of the earth is 1 81 If the radius of the moon is assumed to be one fourth of that of the earth then what is the acceleration due to gravity on the surface of the moon in terms of that on the earth s surface Hence find the escape velocity from the surface of the moon in terms of that from the earth s surface HS 10 esc La 0198 g vesc

A body is projected vertically upwards with a kinetic energy which is half of the minimum kinetic energy required to escape the earth s gravitational attraction Calculate the maximum height attained by the body Radius of the earth R R

A particle of mass M is situated at the centre a spherical shell of same mass and radius a Th gravitational potential at a point situated at distance from the centre will be 1 4GM a 2 3GM a 3 2GM a 4 GN a

1 Find The gravitational field in a region is given by E 31 41 Nkg out the work done in joule in displacing a particle by 1 m along the line 4y 3x 9

around the arth such that its minimum and maximum distance from earth s surface are 800 km and 2400 km respectively Calculate velocity of satellite when its distance from earth is minimum given radius of earth 6400 km 1 7 91 x 10 m s 3 6 x 10 m s 2 7 91 x 10 m s 4 9 x 10 m s

16 The ratio of the distance of two planets from the sun is 1 2 The ratio of their periods of revolution is

The orbital angular momentum of the earth with respect to the sun divided by the mass of the earth is 4 4 x 1015 m s 1 Determine the area enclosed by the orbit of the earth 6 94 x 1022 m

A rocket is launched from a pole of the Earth with velocity Vo where Vo is the orbital velocity of rotation near the surface of the Earth in such a way that it lands at the equator The rocket s time R of flight is T x K Where R Radius of earth g acc due to gravity at the g surface Find value of K