An object of mass $1 \, kg$ is taken to a height from the surface of Earth which is equal to three times the radius of Earth. The gain in potential energy of the object will be $.... \, MJ$ [Given: $g = 10 \, m/s^2$ and radius of Earth $R = 6400 \, km$].

$A$ body of mass $m$ starts falling from a point $2R$ above the Earth's surface. What is its kinetic energy when it has fallen to a point $R$ above the Earth's surface? [$R$ = Radius of Earth,$M$ = Mass of Earth,$G$ = Gravitational Constant]

$A$ body starts from rest from a distance $R_0$ from the centre of the earth. The velocity acquired by the body when it reaches the surface of the earth will be ($R=$ radius of earth,$M=$ mass of earth).

$A$ body is released from a height equal to the radius $(R)$ of the earth. The velocity of the body when it strikes the surface of the earth will be: (Given $g$ = acceleration due to gravity on the earth.)

Two hypothetical planets of masses $m_1$ and $m_2$ are at rest when they are at an infinite distance apart. Because of the gravitational force,they move towards each other along the line joining their centres. What is their speed when their separation is $d$? (Speed of $m_1$ is $v_1$ and that of $m_2$ is $v_2$)

Energy required to move a body of mass $m$ from an orbit of radius $2R$ to $3R$ is