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.

The relay satellite transmits the television signals continuously from one part of the world to another because its:

1. period is greater than the period of rotation of the earth.

2. period is less than the period of rotation of the earth.

3. period has no relation with the period of the earth about its axis.

4. period is equal to the period of rotation of the earth about its axis.