If the gravitational acceleration at surface of Earth is $g$ , then increase in potential energy in lifting an object of mass $m$ to a height equal to half of radius of earth from surface will be

If the distance between the centres of Earth and Moon is $D$ and mass of Earth is $81\, times$ that of Moon. At what distance from the centre of Earth gravitational field will be zero?

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$ . the space around the masses is now filled with a liquid of specific gravity $3$ . The gravitational force between bodies will now be

The magnitudes of gravitational field at distance $r_1$ and $r_2$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. Then

The height at which the weight of a body becomes $1/16^{th}$, its weight on the surface of earth (radius $R$), is

The orbit of geostationary satellite is circular, the time period of satellite depends on $(i)$ mass of the satellite $(ii)$ mass of the earth $(iii)$ radius of the orbit $(iv)$ height of the satellite from the surface of the earth