Gravitation Questions and Answers

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 Ratio of total energy of both is 5 Ratio of kinetic energy of both is 4 Ratio of potential energy of both is 4 Ratio of total energy of both is 4 and ratio of magnitude of potential to kinetic energy is 2

A small satellite of M and radius a revolves around a heavy planet M in a circular orbit such that it always faces the planet during its revolution The closest distance that the planet can get so that the dust particles from the satellite surface does not leave the surface is 1 3 xGM a where x is

Section I Straight Objective Type This section contains 5 multiple choice questions Each question has 4 choices a b c and d out of which ONLY ONE is correct 1 An asteriod of mass m is approaching carth initially at a distance of 10R with speed v It hits the earth with a speed v R and M are radius and mass of earth then 2Gm M R 10 b 1 1 2GM R 2GM R 4 1 10 d v 26m 1 11 Re 10

Two small bodies of masses 1 kg and 4 kg are at rest on a smooth horizontal surface When they are at a separation of 10 m they are released to move under mutual attractive interaction Then which of the following statements is CORRECT A 1kg B 4kg 10m A They will never meet B They will meet at a distance of 6 m from A C To an observer at the centre of mass the particles have equal and opposite momenta D They will meet at a distance of 8 m from B

19 A particle of mass M is situated at the centre of a spherical shell of same mass and radius R The gravitational potential at a point situated at distance from the centre will be R 2 3GM a b R GM d c 2GM R 4GM R 55

The current in the primary circuit of a potentiometer is 0 2 A The specific resistance and cross section of the potentiometer wire are 4 x 107 ohm m and 8 x 10 7 m respectively The potential gradient will be equal to 0 2 V m 1 V m 0 5 V m 0 1 V m

8 Figure shows elliptical path abcd of a planet around the sun S such that the 1 area of triangle csa is the area of 4 the ellipse See figure With db as the major axis and ca as the minor axis If t is the time taken for planet to go over path abe and t2 for path taken over cda then 1 31 1 2 1 21 3 1 31 S C a b

A coil in the shape of equilateral triangle of side 0 02 m is suspended from the vertex such that it is hanging in a vertical plane between the pole pieces of a permanent magnet producing a horizontal magnetic field of 5x10 2 T When a current of 0 1 A passes through it and the magnetic field is parallel to its plane then couple acting on the coil is 1 8 65 x 10 7 N m 2 6 65 x 10 7 N m 3 3 35 x 10 7 N m 4 3 91 x 10 7 N m

A satellite is revolving around earth at a height 2R above earths surface If the satellite is stopped and then released then velocity of body on reaching to earth s surface g is acceleration due to gravity on surface and R is radius of earth 2gR 3 4gR 3 2gR 4gR Marks 4 1

20 An asteroid was located at a distance of 5R with respect to earth s centre and moving with a speed v at an angle of 37 with the line connecting them as shown re 37 1 5v 2 3v 3 2v R Earth If the asteroid just grazes the earth s surface find its maximum speed

Consider a system consisting of three masses on the x axis Mass m1 1 00 kg is at x 1 00 m mass m2 2 00 kg is at x 2 00 m and mass m3 3 00 kg is at x 3 00 m What is the total gravitational potential energy in J of this system O 6 34 10 10 O 5 6 10 10 300 0

A spherical shell is cut into two pieces along a chord as shown in the figure P is a point on the plane of the chord The magnitude of gravitational field at P due to the upper part is 1 and that due to the lower part is 12 What is the relation between them OD 11 12 1 12 1 12 No definite relation

A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius The centre of the ring is directly above the centre of the sphere at a distance r 3 as shown in the figure The gravitational force exerted by the sphere on the ring will be GMm a b 8p GMm 8 c 3 d GMm 4p GMm 8r 3 T 3r 2r

Two particles of mass m and 3m are initially at rest and infinite distance apart Both the particles start moving due to gravitational attraction At any instant their relative velocity of approach is separation at that instant Find n nGm d where d is their

8 Gravitational potential on the surface of an isolated uniform solid sphere of mass M and radius R is found to be V A spherical cavity having radius R 2 is created inside the sphere which is touching the surface of original sphere The cavity is then filled with material having density 16 times that of original sphere A B C and D are consecutive points as shown in the figure each R 2 apart V V V and Vare gravitational potentials found at points A B C and D respectively 82 82 82 Column I A V B V CV D V q r 18 7V 13 4V 19 4V 21 4V 25 4 Column II

D The density of core of a planet is p and that of the outer shell is p The radii of core and that of the planet are R and 2R respectively Gravitational acceleration at the surface of planet is same as at a depth R Then value of is P P2 a 2 3 b 4 5 c 3 2 d 5 4