A satellite is moving with a constant speed $v$ in circular orbit around the earth. An object of mass $‘m’$ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is

A body of mass $m$ is placed on the earth’s surface. It is taken from the earth’s surface to a height $h = 3R$. The change in gravitational potential energy of the body is

The masses and radii of the earth and the moon are $M_1$, $R_1$ and $M_2$,$R_2$ respectively. Their centres are distance $d$ apart. The minimum speed with which particle of mass m should be projected from a point midway between the two centres so as to escape to infinity is :

An object is propelled vertically to a maximum height of $4 R$ from the surface of a planet of radius $R$ and mass $M$. The speed of object when it returns to the surface of the planet is

The masses $m$ in fig. $(A)$ and $(B)$ are identical. The gravitational potential energy  in the two cases are $U_A$ and $U_B$. Then