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

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 which it can go, will be : (R = radius of earth)

Two masses $m_1$ and $m_2$ start to move towards each other due to mutual gravitational force. If distance covered by $m_1$ is $x$, then the distance covered by $m_2$ is

When a body is taken from pole to the equator its weight

Escape velocity at the surface of earth is $11.2\,km/sec$ . If radius of planet is double that of earth but mean density same as that of earth then the escape velocity will be ........ $km/sec$

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