The escape velocity of a body from the earth is about 11.2 km/s. Assuming the mass and radius of the earth to be about 81 and 4 times the mass and radius of the moon respectively, the escape velocity in km/s from the surface of the moon will be:

1. 0.54

2. 2.48

3. 11

4. 49.5

If M is the mass of a planet and R is its radius, then in order to become black hole:

[c is speed of light]

1. $\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}\le \mathrm{c}$

2. $\sqrt{\frac{\mathrm{GM}}{2\mathrm{R}}}\ge \mathrm{c}$

3. $\sqrt{\frac{2\mathrm{GM}}{\mathrm{R}}}\ge \mathrm{c}$

4. $\sqrt{\frac{2\mathrm{GM}}{\mathrm{R}}}\le \mathrm{c}$

The atmosphere on a planet is possible only if: [where v_rms is root mean square speed of gas molecules on planet and v_e is escape speed on its surface]

1. ${\mathrm{v}}_{\mathrm{rms}}={\mathrm{v}}_{\mathrm{e}}$

2. ${\mathrm{v}}_{\mathrm{rms}}>{\mathrm{v}}_{\mathrm{e}}$

3. ${\mathrm{v}}_{\mathrm{rms}}\le {\mathrm{v}}_{\mathrm{e}}$

4. ${\mathrm{v}}_{\mathrm{rms}}<{\mathrm{v}}_{\mathrm{e}}$

When the speed of a satellite is increased by x percentage, it will escape from its orbit where the value of x is:

1. 11.2%

2. 41.4%

3. 27.5%

4. 34.4%

In an orbit if the time of revolution of a satellite is T, then P.E. is proportional to:

1. ${\mathrm{T}}^{1/3}$

2. ${\mathrm{T}}^3$

3. ${\mathrm{T}}^{-2/3}$

4. ${\mathrm{T}}^{-4/3}$

A small satellite is revolving near earth's surface. Its orbital velocity will be nearly:

1. 8 km/s

2. 11.2 km/s

3. 4 km/s

4. 6 km/s

If the potential energy of a satellite is -2 MJ, then the binding energy of the satellite is:

1. 1 MJ

2. 2 MJ

3. 8 MJ

4. 4 MJ

The time period of a polar satellite is about:

1. 24 hr

2. 100 min

3. 84.6 min

4. 6 hr

The mean radius of the earth is R and its angular speed on its axis is $\mathrm{\omega }$. What will be the radius of orbit of a geostationary satellite?

1. ${\left(\frac{\mathrm{Rg}}{{\mathrm{\omega }}^2}\right)}^{1/3}$

2. ${\left(\frac{{\mathrm{R}}^2\mathrm{g}}{{\mathrm{\omega }}^2}\right)}^{1/3}$

3. ${\left(\frac{{\mathrm{R}}^2\mathrm{g}}{\mathrm{\omega }}\right)}^{1/3}$

4. ${\left(\frac{{\mathrm{R}}^2{\mathrm{\omega }}^2}{\mathrm{g}}\right)}^{1/3}$

A satellite of the earth is revolving in a circular orbit with a uniform speed v. If the gravitational force suddenly disappears, the satellite will:

1. continue to move with velocity v along the original orbit.

2. move with a velocity v tangentially to the orbit.

3. fall down with increasing velocity.

4. ultimately come to rest somewhere on the original orbit.