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.

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:

Three identical point masses, each of mass 1 kg lie at three points (0, 0), (0, 0.2 m), (0.2 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 \(\mathrm{m}\) and \(\mathrm{4m}\) are separated by a distance \(\mathrm{r}.\) Their neutral point is at:

1.  $\frac{\mathrm{r}}{2}$ $\mathrm{from}$ $\mathrm{m}$

2.  $\frac{\mathrm{r}}{3}$ $\mathrm{from}$ $4\mathrm{m}$

3.  $\frac{\mathrm{r}}{3}$ $\mathrm{from}$ $\mathrm{m}$

4.  $\frac{\mathrm{r}}{4}$ $\mathrm{from}$ $4\mathrm{m}$

A body of mass m is situated at a distance 4${\mathrm{R}}_{\mathrm{e}}$ above the Earth's surface, where ${\mathrm{R}}_{\mathrm{e}}$ is the radius of the Earth. What minimum energy should be given to the body so that it may escape? 

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: 

The value of acceleration due to gravity at a height of 800 km from the surface of the earth (radius of the earth is 6400 km and value of acceleration due to gravity on the earth's surface is 981 cm/${\mathrm{s}}^2$) is:

Two satellites S₁ and S₂ are revolving around a planet in coplanar and concentric circular orbits of radii R₁ and R₂ in the same direction respectively. Their respective periods of revolution are 1 hr and 8 hr. The radius of the orbit of satellite S₁ is equal to 10⁴ km. Find the relative speed when they are closest to each other. 

1. $2\mathrm{\pi }\times {10}^4$ $\mathrm{kmph}$

2. $\mathrm{\pi }\times {10}^4$ $\mathrm{kmph}$

3. $\frac{\mathrm{\pi }}{2}\times {10}^4$ $\mathrm{kmph}$

4. $\frac{\mathrm{\pi }}{3}\times {10}^4$ $\mathrm{kmph}$ 

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

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 ${\mathrm{R}}^3$, then the time period of revolution T is proportional to:

1. ${\mathrm{R}}^5$

2. ${\mathrm{R}}^3$

3. ${\mathrm{R}}^2$

4. R