The kinetic energy needed to project a body of mass $m$  from the earth's surface (radius $R$ ) to infinity is

An object is taken to height $2 R$ above the surface of earth, the increase in potential energy is $[R$ is radius of earth]

Which of the following statements are true about acceleration due to gravity?

$(a)\,\,'g'$ decreases in moving away from the centre if $r > R$

$(b)\,\,'g'$ decreases in moving away from the centre if $r < R$

$(c)\,\,'g'$ is zero at the centre of earth

$(d)\,\,'g'$ decreases if earth stops rotating on its axis

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

A body weighs $72\, N$ on the surface of the earth. What is the gravitational force(in $N$) on it, at a helght equal to half the radius of the earth$?$