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

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

The potential energy of a satellite having mass m and rotating at a height of 6.4 × ${10}^6$m from the Earth's surface is:

1.  $-0.5$ ${\mathrm{mgR}}_{\mathrm{e}}$

2.  $-{\mathrm{mgR}}_{\mathrm{e}}$

3.  $-2$ ${\mathrm{mgR}}_{\mathrm{e}}$

4.  $4{\mathrm{mgR}}_{\mathrm{e}}$

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? 

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

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: