Gravitation-04-OBJECTIVE UNSOLVED LEVEL – I

UNSOLVED OBJECTIVE LEVEL – I 1. The planet mercury is revolving in an elliptical orbit around the sun C as shown in the figure. K.E. of mercury will be greatest at (a) A (b) B D A (c) C (d) D. E 2. A space ship is launched into a circular orbit close to the earth’s surface. What additional velocity should now be imparted to the space ship in the orbit to over come the gravitational pull (radius of earth = 6400 km and g = 9.8 m/sec2). (a) 4.2 km/sec (b) 4.8 km/sec (c) 3.2 km/sec (d) 3.3 km/sec. 3. An infinite number of masses, each of 1 kg, are placed on the positive x-axis at 1 m, 2 m, 4 m, 8 m, …. from the origin. The value of the gravitational field at the origin due to this distribution is 4G (a) 2G (b) 3 3G (c) 4 (d)  . 4. A satellite is to be stationed in an orbit such that it can be used for relay purposes (such a satellite is called a geostationary satellite) The conditions such a satellite should fulfill is / are (a) its orbit must be in equatorial plane and sence of rotation must be from west to east. (b) its orbital radius must be 42400 km (c) its orbit must not be elliptical and should be circular (d) all the above. 5. A solid sphere of uniform density and radius R applies a gravita- tional force of attraction equal to F1 on a particle placed at A, distance 2R from the centre of the sphere. A spherical cavity of A radiur R/2 is now made in the cavity now applies a gravitional force F2 on the same particle placed at A. The ratio F2 / F1 will be: (a) 1/2 (b) 3 (c) 7 (d) 7/9. 6. Our home planet the Earth suddenly shrinks in size, still remaining perfectly spherical, then which of the following is incorrect : (a) the duration of the day decreases (b) the kinetic energy of rotation about its axis increases (c) every body on its surface becomes lighter (d) the tidal waves on its surface becomes shorter in height. 7. A point P(R 3,0, 0) lies on the axis of a ring of mass M and radius R. The ring is located in y-z plane with its centre at origin O. A small particle of mass m starts from P and reaches O under gravitational attraction only. Its speed at O will be (a) (b) (c) (d) . 8. A particle released at a large distance from a planet reaches the planet only under gravitational attraction and passes through a smooth tunnel through its centre. If ve is the escape velocity of a body at centre of the planet, then the particle’s speed at the centre of the planet is (a) (c) ve 1.5ve (b) (d) 1.5ve 2ve . 9. A solid sphere of uniform density and radius 4 unit is located with Y its centre at the origin of coordinates, O. Two spheres of equal radii of 1 unit, with their centres at A (-2, 0, 0) and B (+2, 0, 0) respec- tively, are taken out of solid sphere, leaving behind spherical cavi- X ties as shown in figure. Choose the incorrect statment (a) the gravitational force due to this object at the origin is ZERO Z (b) the gravitational force at the point B (-2, 0, 0) is ZERO (c) the gravitational potential is the same at all points of the circle y2  z2  36 (d) the gravitational potential is the same at all point on the circle y2  z2  4 . 10. Radius of planet A is twice that of planet B and the density of A is one-third that of B. The ratio of the acceleration due to gravity at the surface of A to that at the surface of B is (a) 2:3 (b) 3:2 (c) 3:4 (d) 4:3. 11. A satellite is moving in a circular orbit around the earth. If gravitational pull suddenly disappears, then it (a) continues to move with the same speed (b) moves with the same speed tangential to the original circular orbit (c) falls down with increasing speed (d) comes to the rest after moving a certain distance along the original path. 12. If the radius of the earth be increased by a factor of 5, by what factor its density be changed to keep the value of g unchanged ? 1 (a) 5 (b) 5 1 (c) (d) 25 . 13. The orbital velocity of an artificial satellite in a circular orbit just above the surface of the earth is v0. The value of the orbital velocity for another satellite orbiting at an altitude of half of earth’s radius is 3  2  (a) (b) 2 0 3 0 (c) 2  (d) 1  . 3 0 3 0 14. The magnitudes of gravitational field at distances r1 and r2 from the centre of a uniform sphere of radius R and mass M are F1 and F2, respectively. Then F r F r2 1  1 if r  R and r  R 1  2 if r  R and r  R (a) F2 r2 (b) 2 1 2 2 1 (c) F1  r1 if r F2 2  R and r2  R (d) F1 F2 r2  1 if r1 2  R and r2  R . UNSOLVED OBJECTIVE LEVEL – II 1. Two partices of mass m1 and m2 are initially are rest at infinite distance find their velocity of ap- proach due to gravitational attraction, when separation is d, (a) (b) (c) (d) . 2. A satellite of mass 1000 kg is rotating around the earth in circular orbit of radius 3R. What extra energy should be given to this satellite if it is to be lifted into an orbit of radius 4R. (a) (c) 2.614 1924 J 1.8141920 J (b) (d) 1.8141019 J 2.614 199 J . 3. What is acceleration due to gravity at the surface of mars if its diameter is 6760 km and mass one tength that of earth. The diameter of earth is 12742 km and acceleration due to gravity on earth is 9.8 m/sec2 (a) 4.18 m/sec2 (b) 3.03 m/sec2 (c) 4.58 m/sec2 (d) 3.48 m/sec2. 4. Imagine a light planet revolving around a very massive star in circular orbit of radius r with a period of revolution T. On what power of ‘r’, will the square of time period depend if the gravitation force of attraction between the planet and the star is praportional to r5 / 2 (a) (c) T2  r7 / 2 T2  r1 / 2 (b) (d) T2  r5/ 2 T2  r3 / 2 . 5. The rotation of the earth having radius R about its axis speeds upto a value such that a man at laltitude angle 600 feels weightless. The duration of the day in such case will be (a) 8 (c)  (b) 8 (d) 4 . 6. Consider an infinite plane sheet of mass with surface mass density  . The magnitude of gravitation field intensity at a point P located at perpendicular distance r from such sheet is (a) 1 2G 2 (b) G (c) 2G (d) 4G . 7. A projectile is fired upwards from the surface of the earth with a velocity kVe where k is a constant whose value is less than one and Ve is the escape velocity. Neglecting air resistance, the maximum height to which it will rises is ? K R (a) (c) R  K K R 2  K2 (b) (d) (d) R 2  K2 K2R 1  K 2 . 8. A homogeneous bar of length L and mass M is at a distance h from m M a point mass m as shown. The force on m is F. Then h L (a) (c) F  GMm (h  L)2 F GMm h(h  L) (b) (d) F  GMm h 2 F  GMm . L2 9. A body suspended on a spring balance in a ship weighs W, when ship is at rest. When the ship begins to move along the equator from west to east with the velocity v, the scale reading is approximately equal to (  to angular velocity of earth)  v2  (a) W (b) W1      2v   2vm  (c) W 1  g  (d) W 1 W  .     10. A particle of mass m is located at a distance r from the centre of a shell of mass M and radius R. The force between the shell and mass is F(r). The plot of F(r) vs r is F(r) F(r) (a) r (b) r (c) r (d) . r 11. A shell of mass M and radius R has a point mass m placed at a distance r from its centre. The gravitational potential energy U (r) vs r will be r r (a) U(r) (b) U(r) r (c) – r (d) . U(r) U(r) 12. A particle of mass m is transferred from the centre of the base of a uniform solid hemisphere of mass M and radius R to infinity. The work performed in the process by the gravitational force exerted on the particle by the hemisphere is (a) (c)  GMm R  3 GMm 2 R (b) (d)  1 GMm 2 R  3 GMm . 4 R 13. A body is launched with a velocity less than escape velocity. The total mechanical energy is (a) positive (b) negative (c) zero (d) may be positive or negative. 14. The gravitational force between a point like mass M and an infinitely long, thin rod of linear mass density  at a perpendicular distance L from M is MG 1 MG (a) L 2MG (b) 2 L (c) L (d) infinite. 15. In some region, the gravitational field is zero. The gravitational potential in this region (a) must be zero (b) cannot be zero (c) must be constant (d) may be variable.