A satellite is moving very close to a planet of density \(\rho.\) The time period of the satellite is:
1. \(\sqrt{\frac{3 \pi}{ρG}}\)
2. \(\left(\frac{3 \pi}{ρG}\right)^{3 / 2}\)
3. \(\sqrt{\frac{3 \pi}{2 ρG}}\)
4. \(\left(\frac{3 \pi}{2 ρG}\right)^{3 / 2}\)

The gravitational potential difference between the surface of a planet and 10 m above is 5 J/kg. If the gravitational field is supposed to be uniform, the work done in moving a 2 kg mass from the surface of the planet to a height of 8 m is

1.  2J

2.  4J

3.  6J

4.  8J

Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

1.  $-\frac{5\mathrm{Gm}}{\mathrm{r}}$

2.  $-\frac{6\mathrm{Gm}}{\mathrm{r}}$

3.  $-\frac{9\mathrm{Gm}}{\mathrm{r}}$

4.  0

The satellite of mass m orbiting around the earth in a circular orbit with a velocity v. The total energy will be:

1.  $\frac{3}{4}{\mathrm{mv}}^2$

2.  $\frac{1}{2}{\mathrm{mv}}^2$

3.  $-\frac{1}{2}{\mathrm{mv}}^2$

4.  ${\mathrm{mv}}^2$

Kepler's second law regarding constancy of the areal velocity of a planet is a consequence of the law of conservation of:

1. Energy

2. Linear momentum

3. Angular momentum

4. Mass

Weightlessness experienced while orbiting the earth in a space-ship is the result of:

1. Inertia                        
2. Acceleration
3. Zero gravity
4. Freefall towards the earth

The escape velocity for a rocket from the earth is \(11.2\) km/s. Its value on a planet where the acceleration due to gravity is double that on the earth and the diameter of the planet is twice that of the earth (in km/s) will be:

If g is the acceleration due to gravity at the earth's surface and r is the radius of the earth, the escape velocity for the body to escape out of the earth's gravitational field is:

1. gr                                       

2. $\sqrt{2gr}$

3. g/r                                       

4. r/g

The escape velocity of a particle of mass m varies as:

1. $m^2$                                   

2. m

3. $m^0$                                   

4. $m^{-1}$