The height at which the weight of a body becomes \(\left ( \frac{1}{16} \right )^\mathrm{th}\) of its weight on the surface of the earth (radius \(R\)) is:
1. \(5R\)
2. \(15R\)
3. \(3R\)
4. \(4R\)

A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force:

The dependence of acceleration due to gravity \('g'\) on the distance \('r'\) from the centre of the earth, assumed to be a sphere of radius \(R\) of uniform density, is as shown in figure below:

(a)		(b)
(c)		(d)

                    
The correct figure is:
1. \(a\)

2. \(b\)

3. \(c\)

4. \(d\)

The density of a newly discovered planet is twice that of Earth. If the acceleration due to gravity on its surface is the same as that on Earth, and the radius of Earth is \(R,\) what will be the radius of the new planet?

When a body of weight \(72\text{ N}\) moves from the surface of the Earth at a height half of the radius of the earth, then the gravitational force exerted on it will be:

1. \(36\text{ N}\)

2. \(32\text{ N}\)

3. \(144\text{ N}\)

4. \(50\text{ N}\)

If the radius of the earth shrinks by 1%, then for acceleration due to gravity, there would be:
1. No change at the poles
2. No change at the equator
3. Maximum change at the equator
4. Equal change at all locations

For moon, its mass is \(\frac{1}{81}\) of Earth's mass and its diameter is \(\frac{1}{3.7}\) of Earth's diameter. If acceleration due to gravity at Earth's surface is \(9.8~\text{m/s}^2,\) then at the moon, its value is: