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

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. \(T \propto \frac{r^5}{GM}\)
2. \(T \propto \sqrt{\frac{r^3}{GM}}\)
3. \(T \propto \sqrt{\frac{r}{\frac{GM^2}{3}}}\)
4. \(T \propto \sqrt{\frac{r^3}{\frac{GM^2}{4}}}\)