The gravitational potential energy of an isolated system of three particles, each of mass \(m\) placed at three corners of an equilateral triangle of side \(l\) is: 

1.	\(-Gm \over {l}^2\)	2.	\(-Gm^2 \over 2{l}\)
3.	\(-2Gm^2 \over {l}\)	4.	\(-3Gm^2 \over {l}\)

Two satellites \(S_1\)​ and \(S_2\)​ move in the same direction in coplanar, concentric circular orbits of radii \(R_1\)​ and \(R_2.\) Their orbital periods are \(1~\text{hr}\) and \(8~\text{hr}\) respectively. If \(R_1=10^4~\text{km},\) what is their relative speed when they are closest to each other?

The potential energy of a satellite having mass \(m\) and rotating at a height of \(6.4\times 10^{6}~\text{m}\) from the Earth's surface is:
1. \(-0.5mg R_e\)
2. \(-mg R_e\)
3. \(-2mg R_e\)
4. \(4mg R_e\)

Two particles of mass \(m\) and \(4m\) are separated by a distance \(r.\) Their neutral point is at:
1. \(\frac{r}{2}~\text{from}~m\)
2. \(\frac{r}{3}~\text{from}~4m\)
3. \(\frac{r}{3}~\text{from}~m\)
4. \(\frac{r}{4}~\text{from}~4m\)

A satellite is revolving around the earth with speed \(v_0\). If it is stopped suddenly, then with what velocity will the satellite hit the ground? (\(v_e\)= escape velocity from the earth's surface)
1. \(\sqrt{v_{e}^{2} - v_{0}^{2}}\)
2. \(\sqrt{v_{e}^{2}-2 v_{0}^{2}}\)
3. \(\sqrt{v_{e}^{2}-3 v_{0}^{2}}\)
4. \(\sqrt{v_{e}^{2}-\frac{v_{0}^{2}}{2}}\)

Three identical point masses, each of mass \(1~\text{kg}\) lie at three points \((0,0),\)  \((0,0.2~\text{m}),\)  \((0.2~\text{m}, 0).\) The net gravitational force on the mass at the origin is:
1. \(6.67\times 10^{-9}(\hat i +\hat j)~\text{N}\)
2. \(1.67\times 10^{-9}(\hat i +\hat j) ~\text{N}\)
3. \(1.67\times 10^{-9}(\hat i -\hat j) ~\text{N}\)
4. \(1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}\)

A planet moves around the Sun \(S\) in an elliptical orbit, as shown in the figure. If its distances from the Sun at points \(A\) and \(B\) are \(r_1\)​ and \(r_2\)​ respectively, what is the ratio of its linear momentum at \(A\) to that at \(B\)?

If \(R\) represents the orbital radius of a planet and \(T\) its orbital period, which of the following graphs correctly depicts the relationship between \(R\) and \(T\) for a planet revolving around the Sun?

1.		2.
3.		4.

If the speed of an artificial satellite revolving around the earth in a circular orbit be \(2 \over 3\) of the escape velocity from the surface of earth then its altitude above the surface of the earth is