Gravitation

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

Match List I with List II : (Where a = radius of planet orbit, r = radius of planet, M = mass of Sun, m = mass of planet) Choose the correct answer from the options given below :

1. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
2. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
3. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
4. (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius of orbit of the satellite is : (Given: Radius of geo-stationary orbit for earth is 4.2 104 km)

1. 1.68 105 km
2. 1.4 104 km
3. 8.4 104 km
4. 1.05 104 km

A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is :

1. GmM 2L2
2. GMm 2L2
3. 0
4. 2GmM L2