In a satellite if the time of revolution is T, then K.E. is proportional to 

(1) $\frac{1}{T}$                       

(2) $\frac{1}{T^2}$

(3) $\frac{1}{T^3}$                       

(4) $T^{\raisebox{1ex}{$-2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

The period of a satellite in a circular orbit of radius R is T, the period of another satellite in a circular orbit of radius 4R is

(1)4T                                                   

(2)$\frac{T}{4}$

(3)8T                                                   

(4)$\frac{T}{8}$

If the height of a satellite from the earth is negligible in comparison to the radius of the earth R, the orbital velocity of the satellite is 

(1) gR                       

(2) gR/2

(3) $\sqrt{g/R}$                

(4) $\sqrt{gR}$

Choose the correct statement from the following.

The radius of the orbit of a geostationary satellite depends upon -

(1) Mass of the satellite, its time period and the gravitational constant

(2) Mass of the satellite, mass of the earth and the gravitational constant

(3) Mass of the earth, the mass of the satellite, time period of the satellite and the gravitational constant

(4) Mass of the earth, time period of the satellite and the gravitational constant

A planet moves around the sun. At a given point P, it is closest from the sun at a distance $d_1$ and has a speed $v_1$. At another point Q,  when  it is farthest from the sun at a distance $d_2$, its speed will be

(1)$\frac{{d_1}^2{v}_1}{{d_2}^2}$                                             

(2)$\frac{d_2{v}_1}{d_1}$

(3)$\frac{d_1{v}_1}{d_2}$                                               

(4)$\frac{{d_2}^2{v}_1}{{d_1}^2}$

A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1%, its speed will 

(1) Increase by 1%                       

(2) Increase by 0.5%

(3) Decrease by 1%                     

(4) Decrease by 0.5%

Orbital velocity of an artificial satellite does not depend upon 

(1) Mass of the earth

(2) Mass of the satellite

(3) Radius of the earth

(4) Acceleration due to gravity

The time period of a geostationary satellite is

(1) 24 hours                         

(2) 12 hours

(3) 365 days                         

(4) One month

The orbital velocity of Earth's satellite near the surface is 7 km/s. When the radius of the orbit is 4 times more than that of Earth's radius, then orbital velocity in that orbit is:

(1) 3.5 km/s                         

(2) 7 km/s

(3) 72 km/s                           

(4) 14 km/s

A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts
(1) 1/3                           

(2) 1/2

(3) 1/4                           

(4) 1/5