A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. ($v_e$ is escape velocity and $k < 1$). If air resistance is considered to be negligible then the maximum height from the centre of earth to whichit can go, will be : ($R =$ radius of earth)

If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth, 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]

A rocket is projected in the vertically upwards direction with a velocity kve where $v_e$ is escape velocity and $k < 1$. The distance from the centre of earth upto which the rocket will reach, will be

The escape velocity of a body from earth's surface is $v_e$ . The escape velocity of the same body from a height equal to $R$ from the earth's surface will 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