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

Two identical satellites are at R and 7R away from earth surface, the wrong statement is (R = Radius of earth)

(1) Ratio of total energy will be 4

(2) Ratio of kinetic energies will be 4

(3) Ratio of potential energies will be 4

(4) Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2

For a satellite, the escape velocity is 11 km/s. If the satellite is launched at an angle of 60° with the vertical, then escape velocity will be: 

(1) 11 km/s                        

(2) $11\sqrt{3} km/s$

(3) $\frac{11}{\sqrt{3}} km/s$                     

(4) 33 km/s

The mean radius of the earth is R, its angular speed on its own axis is $\omega$ and the acceleration due to gravity at the earth's surface is g. The cube of the radius of the orbit of a geostationary satellite will be -

(1) $R^{2}g/\omega$                   

(2) $R^2{\omega }^2/g$

(3) $Rg/{\omega }^2$                    

(4) $R^{2}g/{\omega }^2$

A satellite whose mass is m, is revolving in a circular orbit of radius r, around the earth of mass M. Time of revolution of the satellite is:

1. $\mathrm{T}\propto \frac{{\mathrm{r}}^5}{\mathrm{GM}}$

2. $\mathrm{T}\propto \sqrt{\frac{{\mathrm{r}}^3}{\mathrm{GM}}}$

3. $\mathrm{T}\propto \sqrt{\frac{\mathrm{r}}{{\mathrm{GM}}^2/3}}$

4. $\mathrm{T}\propto \sqrt{\frac{{\mathrm{r}}^3}{{\mathrm{GM}}^2/4}}$

Suppose the gravitational force varies inversely as the ${\mathrm{n}}^{\mathrm{th}}$ power of distance then the time period of a planet in circular orbit of radius R around the sun will be proportional to:

1. ${\mathrm{R}}^{\left(\frac{\mathrm{n}+1}{2}\right)}$                 

2. ${\mathrm{R}}^{\left(\frac{\mathrm{n}-1}{2}\right)}$

3. ${\mathrm{R}}^{\mathrm{n}}$                         

4. ${\mathrm{R}}^{\left(\frac{\mathrm{n}-2}{2}\right)}$  

The orbital speed of an artificial satellite very close to the surface of the earth is $V_o$. Then the orbital speed of another artificial satellite at a height equal to three times the radius of the earth is 

(a) $4 V_0$                    (b) $2 V_0$

(c) $0.5V_0$                   (d) $4 V_0$

The distance of a geostationary satellite from the centre of the earth (Radius R = 6400 km) is nearest to:

(1) 5R                                     (2) 7R

(3) 10R                                   (4) 18R