1 kg of sugar has maximum weight:
1. at the pole.
2. at the equator.
3. at a latitude of 45$°$.
4. in India.

A body is thrown vertically upwards with an initial speed $\sqrt{gR}$, where R is the radius of the earth. The maximum height reached by the body from the surface of the earth is:

1.  $\frac{\mathrm{R}}{2}$

2.  $\frac{3\mathrm{R}}{2}$

3.  R

4.  $\frac{\mathrm{R}}{4}$

A particle is located midway between two point masses each of mass \(\mathrm{M}\) kept at a separation \(2\mathrm{d}.\) The escape speed of the particle is: (neglect the effect of any other gravitational effect)

1.  $\sqrt{\frac{2\mathrm{GM}}{\mathrm{d}}}$

2.  $2\sqrt{\frac{\mathrm{GM}}{\mathrm{d}}}$

3.  $\sqrt{\frac{3\mathrm{GM}}{\mathrm{d}}}$

4.  $\sqrt{\frac{\mathrm{GM}}{2\mathrm{d}}}$

Three identical particles each of mass M are located at the vertices of an equilateral triangle of side a. The escape speed of one particle will be:

1.  $\sqrt{\frac{4\mathrm{GM}}{\mathrm{a}}}$

2.  $\sqrt{\frac{3\mathrm{GM}}{\mathrm{a}}}$

3.  $\sqrt{\frac{2\mathrm{GM}}{\mathrm{a}}}$

4.  $\sqrt{\frac{\mathrm{GM}}{\mathrm{a}}}$

The escape velocities from the surface of two planets of the same mass are in the ratio of $1:\sqrt{2}$. The ratio of their densities is:

Two identical hollow spheres of negligible thickness are placed in contact with each other. The force of gravitation between the spheres will be proportional to (R = radius of each sphere):

1.  R

2.  $R^2$

3.  $R^4$

4.  $R^3$

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

When a planet revolves around the sun in an elliptical orbit, then which of the following remains constant?

A satellite of mass 1000 kg revolves in a circular orbit around the earth with a constant speed of 100 m/ s. The total mechanical 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: