Gravitation

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected.

1. 3 days
2. 27 days
3. 81 days
4. 1 day

A satellite of mass M2 is revolving around earth in a circular orbit at a height of R3 from earth surface. The angular momentum of the satellite is M GMRx. The value of x is , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)

A small point of mass m is placed at a distance 2R from the centre ' O ' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is F1. A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be F2. The value of ratio F1:F2 is [figure]

1. 11 : 10
2. 12 : 11
3. 16 : 9
4. 12 : 9

An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km. From earth's surface to the orbit, the change in total mechanical energy of the ball is x GMe m21Re. The value of x is (take Re = 6370 km) :

1. 12
2. 11
3. 9
4. 10

A satellite of 103 kg mass is revolving in circular orbit of radius 2R. If 104R6 J energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use g = 10 m/s2, R = radius of earth)

1. 4R
2. 6R
3. 2.5R
4. 3R

Two planets A and B having masses m1 and m2 move around the sun in circular orbits of r1 and r2 radii respectively. If angular momentum of A is L and that of B is 3L, the ratio of time period ( TATB ) is:

1. ( r2r1 ) 32
2. 27 ( m1m2 )3
3. ( r1r2 )3
4. 127 ( m2m1 )3

Two satellites A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3v, the speed of B will be :

1. 6v
2. 43v
3. 3v
4. 12v

To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is RE, g = acceleration due to gravity on the surface of earth):

1. 12mgRE
2. 4mgRE
3. mgRE
4. 2mgRE

Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

1. 75 N
2. 375 N
3. 300 N
4. 225 N

A simple pendulum doing small oscillations at a place R height above earth surface has time period of T1 = 4 s. T2 would be its time period if it is brought to a point which is at a height 2R from earth surface. Choose the correct relation [R = radius of earth] :

1. 3T1 = 2T2
2. T1 = T2
3. 2T1 = 3T2
4. 2T1 = T2