If the Earth's mass were doubled and its radius were halved, the acceleration due to gravity at its surface would become:

Two spherical balls each of mass 2 kg are placed at 3 cm apart. Find the gravitational force of attraction between them is [Newton] nearly

Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a min $100\,km$ below the earth’ surface (Given $R = 6400\;km$)

A metre of mass $M$ breaks up into two parts. The mass of one part is $m$. For a given separation $r$, the mutual force of gravitation between the two parts will be maximum when

If mass of a body is M on the earth surface, then the mass of the same body on the moon surface is

The gravitational field in a region is given by the equation $E=(5 i+12 j) \mathrm{N} / \mathrm{kg}$. If a particle of mass $2 \mathrm{~kg}$ is moved from the origin to the point $(12 \mathrm{~m}, 5 \mathrm{~m})$ in this region, the change in the gravitational potential energy is

A satellite is orbiting Earth at a radius 'r' from its center. If the radius is doubled to '2r', how does the gravitational potential experienced by the satellite change?

A body of mass $m$ is projected from earth surface with speed ${v = \,2\sqrt {gR} }$ (where $R$ is the radius of earth). Find its speed at very far (infinite) from earth’s surface:-

The acceleration due to gravity is $g$ at a point distant $r$ from the centre of earth of radius $R$. If $r < R$, then

The mass density of a spherical galaxy varies as $\frac{K}{r}$ over a large distance $r$ from its centre. In that region, a small star is in a circular orbit of radius R. Then, the period of revolution $T$ depends on $R$ as

Sun is about 330 times heavier and 100 times bigger in radius than earth. The ratio of mean density of the sun to that of earth is