A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass \(= 5.98\times 10^{24}~\text{kg}\)) have to be compressed to be a black hole?
1. \(10^{-9}~\text{m}\)
2. \(10^{-6}~\text{m}\)
3. \(10^{-2}~\text{m}\)
4. \(100​~\text{m}\)

Dependence of intensity of gravitational field \((\mathrm{E})\) of the earth with distance \((\mathrm{r})\) from the centre of the earth is correctly represented by: (where \(\mathrm{R}\) is the radius of the earth)

1.		2.
3.		4.

A body of mass \(m\) is taken from the Earth’s surface to the height equal to twice the radius \((R)\) of the Earth. The change in potential energy of the body will be: 

The height at which the weight of a body becomes \(\left ( \frac{1}{16} \right )^\mathrm{th}\) of its weight on the surface of the earth (radius \(R\)) is:
1. \(5R\)
2. \(15R\)
3. \(3R\)
4. \(4R\)

A spherical planet has a mass \(M_p\) and diameter \(D_p\)${\mathrm{}}_{}$. A particle of mass \(m\) falling freely near the surface of this planet will experience acceleration due to gravity equal to:
1. \(\frac{4GM_pm}{D_p^2}\)
2. \(\frac{4GM_p}{D_p^2}\)
3. \(\frac{GM_pm}{D_p^2}\)
4. \(\frac{GM_p}{D_p^2}\)

A geostationary satellite is orbiting the earth at a height of \(5R\) above the surface of the earth, \(R\) being the radius of the earth. The time period of another satellite in hours at a height of \(2R\) from the surface of the earth is:
1. \(5\)
2. \(10\)
3. \(6\sqrt2\)
4. \(\frac{6}{\sqrt{2}}\)

A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the linear velocities at these points respectively, then the ratio $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}$ is:

1.  ${\mathrm{r}}_2/{\mathrm{r}}_1$

2.  ${\left({\mathrm{r}}_2/{\mathrm{r}}_1\right)}^2$

3.  ${\mathrm{r}}_1/{\mathrm{r}}_2$

4.  ${\left({\mathrm{r}}_1/{\mathrm{r}}_2\right)}^2$

A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force:

The radii of circular orbits of two satellites A and B of the earth are \(4R\) and \(R\) respectively. If the speed of satellite A is \(3v,\) then the speed of satellite B will be:
1. \(3v/4\)
2. \(6v\)
3. \(12v\)
4. \(3v/2\)