Mass and radius of the earth is M and R respectively, then the gravitational potential at a distance R/3 from the centre of the earth is

1.  $-\frac{\mathrm{GM}}{\mathrm{R}}$

2.  $-\frac{3\mathrm{GM}}{\mathrm{R}}$

3.  $-\frac{11}{9}\frac{\mathrm{GM}}{\mathrm{R}}$

4.  $-\frac{13}{9}\frac{\mathrm{GM}}{\mathrm{R}}$

Starting from the centre of the earth, having radius \(R,\) the variation of \(g\) (acceleration due to gravity) is shown by:

1.		2.
3.		4.

If the mass of the sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following statements would not be correct?

The kinetic energies of a planet in an elliptical orbit around the Sun, at positions \(A,B~\text{and}~C\) are \(K_A, K_B~\text{and}~K_C\) respectively. \(AC\) is the major axis and \(SB\) is perpendicular to \(AC\) at the position of the Sun \(S\), as shown in the figure. Then:
                 

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: 

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. \(\frac{GM_p}{D_p^2}\)