Let g be the acceleration due to gravity at the earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities the same, then

1.  g decreases by 2% and K decreases by 4%

2.  g decreases by 4% and K increases by 2%

3.  g increases by 4% and K increases by 4%

4.  g decreases by 4% and K increases by 4%

Distance of geostationary satellite from the center of the Earth $(R_e=6400 km)$ in terms of $R_e$ is-

1. $13.76 R_e$                        

2. $10.76 R_e$

3. $6.59 R_e$                            

4. $2.56 R_e$

Energy required to move a body of mass m from an orbit of radius 2R to 3R is

1.     $GMm/12R^2$               

2.    $GMm/3R^2$

3.     $GMm/8R$                 

4.     $GMm/6R$

Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to -

1. $\frac{1}{R}$                      

2. $\frac{1}{\sqrt{R}}$

3. R                         

4.  $\frac{1}{R^{3/2}}$

Two satellite A and B, ratio of masses 3 : 1 are in circular orbits of radii r and 4r. Then ratio of total mechanical energy of A to B is 

1. 1 : 3                             

2. 3 : 1

3. 3 : 4                             

4. 12 : 1

A satellite moves round the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is -

1. 8 R                           

2. 4R

3. 2R                             

4. R

At what height from the surface of earth the gravitation potential and the value of g are $-5.4\times {10}^{7}J k{g}^{-2}$ and $6.0 m{s}^{-2}$ respectively? (Take, the radius of earth as 6400 km.)

1. 1600 km             

2. 1400 km 

3. 2000 km             

4. 2600 km

A remote sensing satellite of earth revolves in a circular orbit at a height of 0.25 x 10⁶ m above the surface of earth. If earth’s radius is 6.38x10⁶ m and g=9.8ms^-1, then the orbital speed of the satellite is

1. 7.76kms^-1

2. 8.56kms^-1

3. 9.13kms^-1

4. 6.67kms^-1

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth. Then,

1. the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant

2. the total mechanical energy of S varies periodically with time

3. the linear momentum of S remains constant in magnitude

4. the acceleration of S is always directed towards the centre of the earth

Which one of the following plots represent

the variation of gravitational field on a 

particle at distance r, due to a thin 

spherical shell of radius R? (r is measured 

from the centre of the spherical shell).

1.  2.

3.    4.