Title 08. GRAVITATION.pdf ✅

PAPER 1 (1.) The value of 'g' on the surface of another planet whose mass as well as radius is twice that of earth is ( e g = value on earth) : (1) equal to e g (2) twice e g (3) half of e g (4) 2 times e g (2.) The value of ' g ' at a place is 2 9.8 ms− , if the earth shrinks uniformly (without changing its mass or centre) to half its size the value of ' g ' at the same point will now be : (1) 2 9.8 m s− (2) 2 19.6 m s− (3) 2 4.9 m s− (4) zero (3.) The weight of the body at the centre of earth is : (1) zero (2) infinity (3) 9.8 times the weight on the surface (4) None of these (4.) To what height the body is to be raised so that force of gravity on it is 1% of the value on the surfaace of earth? (Radius of earth is 6400 km ) : (1) 6400 km (2) 12800 km (3) 57600 km (4) 3200 km (5.) At what height the value of ' g ' is half that on the surface : (1) R (2) 2R (3) 0.414R (4) None of these (6.) If radius of earth shrinks by 2% (mass remaining same), how much will be the change in value of g at the surface of earth : (1) 2% (2) 1% (3) 4% (4) 3% (7.) Minimum work done to shift a body of mass m from a circular orbit of 2R to a higher orbit of radius 3R around the earth ( R = Radius of earth) : (1) GMm 4R (2) GMm 6R (3) GMm 8R (4) GMm 12R (8.) The period of satellite in a circular orbit of radius R0 is T , the period of another satellite in circular orbit of radius 0 4R is : (1) T /4 (2) T /8 (3) 4 T (4) 8 T (9.) The time period of simple pendulum in a satellite is : (1) infinite (2) zero (3) 2sec (4) Cannot be calculated (10.) A satellite moving in a circular orbit of radius R0 round the earth of mass M and radius R , has angular velocity :
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(1) 3 0 GM R (2) 3 GMR0 (3) 3 R0 GM (4) None of these (11.) Ratio of K.E. required for the satellite to escape the earth's surface to the K.E. required to orbit just close to the earth is : (1) 1:1 (2) 2:1 (3) 1: 2 (4) None of these (12.) Two identical metal spheres of same material of density 'd' are touching each other. What is the gravitational force of attraction between them ? (1) 4 2 2 4 9 G d R  (2) 9 2 2 4 G d R 4  (3) 4 2 2 9 G d R  (4) 9 2 2 4 G d R  (13.) Two small bodies initially both at rest and free to move from a distance of 1 m from each other, are subjected to only their gravitational force of attraction. They approach each other and collide and do not separate. In respect of this collision which of the following statement is true : (1) The total gravitational potential energy of the two masses has increased on collision (2) The total gravitational potential energy of the two masses has decreased on collision (3) The law of conservation of energy does not hold good (4) The force of gravitational attraction vanishes when the bodies come in contact. (14.) A spaceship is moving close to earth. What additional velocity is to be imparted to it so as to make it escape the earhtls gravitational pull? ) 2 (g = 9.8 ms ;R 6400 km − = (1) 1 3.28 km s− (2) 1 0.328 km s− (3) 1 32.8 km s− (4) None of these (15.) With what velocity should a body be thrown up so that it rises to a height equal to the radius of the earth ? ( 2 g 10 ms− = at the surface) (1) 1 8000 m s− (2) 1 6400 m s− (3) 1 1600 m s− (4) 1 1000 m s− (16.) A body released from a height ' h ' takes time t sec. to reach the earth's surface. The same body released from same height will take how much time to reach the moon's surface? ( 6 e m g g h   =     is very small) (1) t sec (2) t 6sec (3) t 6sec (4) sec 6 t (17.) A body is thrown up with a velocity 10% more than the escape velocity e v . When the body escapes the gravitational pull of the earth the velocity still left in the body is : (1) e 0.1v (2) 0.229 e v (3) 0.458 e v (4) 0.20 e v
(18.) How much deep inside the earth (radius R ) should a man go, so that his weight becomes one-fourth of that on earth's surface : (1) 4 R (2) 2 R (3) 3 4 R (4) None of these. (19.) Two bodies of masses 3 10 kg and 5 10 kg are separated by a distance of 2 m . At what distance from smaller body will the intensity of the gravitational field is zero? (1) 1 m 11 (2) 2 m 11 (3) 3 11 m (4) 2 m 9 (20.) A projectile is fired with a speed less than the escape speed. Its mechanical energy is : (1) Positive at all positions (2) Negative at all positions (3) Positive at all positions except the highest point where it is zero (4) None of the above. (21.) The force of gravity is the least at : (1) the equator (2) the poles (3) a point in between equator and poles (4) None of the above (22.) The weight of body at a height equal to the radius of the earth is W , its weight at a height equal to three times the radius of the earth will be : (1) 2 W (2) 3 W (3) 4 W 3 (4) 4 W (23.) The distance of planets Neptune and Saturn are 13 10 and 12 10 meters respectively from the sun. Assuming their orbits to be circular, their periodic times are in the ratio : (1) 10:1 (2) 100:1 (3) 1000:1 (4) 10 10 :1 (24.) The escape velocity of a projectile from the surfac of earth is 1 11.2 km s− . A body is projected with thrice this speed. What is the speed of the body far from earth? (1) 1 31.68 km s− (2) 1 3.168 km s− (3) 1 316.8 km s− (4) None of these (25.) If the gravitational force varies inversely as the nth power of the distance then the time period T of a satellite revolving in a circular orbit round the earth at distance r is proportional to : (1) 1 2 ( ) n r + (2) 1 2 ( ) n r − (3) n 1 1 r + (4) n 1 1 r − (26.) Earth is revolving around the sun. If the distance of the earth from the sun is reduced to 1/ 4 th of the present distance then the year length reduced to : (1) 1/ 4 (2) 1/ 8 (3) 1/ 2 (4) 1/ 6