A satellite is revolving around the earth with speed ${\mathrm{v}}_0$. If it is stopped suddenly, then with what velocity will the satellite hit the ground? (${\mathrm{v}}_{\mathrm{e}}$ = escape velocity from the earth's surface)

1.  $\sqrt{v_e^2 - v_0^2}$

2.  $\sqrt{v_e^2 - 2v_0^2}$

3.  $\sqrt{v_e^2 - 3v_0^2}$

4.  $\sqrt{v_e^2 - \frac{v_0^2}{2}}$

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. \(\frac{r}{4}~\text{from}~4m\)

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 \(1\) hr and \(8\) hr. The radius of the orbit of satellite \(S_1\) is equal to \(10^4\) 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. \(\frac{\pi}{3} \times 10^4~\text{kmph}\)

Three identical point masses, each of mass \(1\) 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