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 satellites \(S_1\) and \(S_2\) are revolving around a planet in coplanar and concentric circular orbits of radii \(R_1\) and \(R_2\) in the same direction respectively. Their respective periods of revolution are \(1~\text{hr}\) and \(8~\text{hr}.\) The radius of the orbit of satellite \(S_1\) is equal to \(10^4~\text{km}.\) Find the relative speed when they are closest to each other. 
1. \(2\pi \times 10^4~\text{kmph}\)
2. \(\pi \times 10^4~\text{kmph}\)
3. \(\frac{\pi}{2} \times 10^4~\text{kmph}\)
4. \(\frac{\pi}{3} \times 10^4~\text{kmph}\)

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. \(1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}\)

The figure shows a planet in an elliptical orbit around the sun \((S).\) The ratio of the momentum of the planet at point \(A\) to that at point \(B\) is:

                           
1. \(\frac{r_1}{r_2}\)
2. \(\frac{r_{1}^{2}}{r_{2}^{2}}\)
3. \(\frac{r_2}{r_1}\)
4. \(\frac{r_{2}^{2}}{r_{1}^{2}}\)

If \(R\) is the radius of the orbit of a planet and \(T\) is the time period of the planet, then which of the following graphs correctly shows the motion of 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