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. \(\frac{r_{2}^{2}}{r_{1}^{2}}\)

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

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. \(\frac{r}{4}~\text{from}~4m\)

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. \(\frac{\pi}{3} \times 10^4~\text{kmph}\)

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.

A satellite of mass \(m\) revolving around the earth in a circular orbit of radius \(r\) has its angular momentum equal to \(L\) about the centre of the earth. The potential energy of the satellite is: 
1. \(- \frac{L^{2}}{2 mr}\)
2. \(- \frac{2L^{2}}{mr^2}\)
3. \(- \frac{3L^{2}}{m^2r^2}\)
4. \(- \frac{L^{2}}{mr^2}\)

A planet is revolving around a massive star in a circular orbit of radius \(R\). If the gravitational force of attraction between the planet and the star is inversely proportional to \(R^3,\) then the time period of revolution \(T\) is proportional to:
1. \(R^5\)
2. \(R^3\)
3. \(R^2\)
4. \(R\)