$A$ 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]

Under the influence of a central force,which of the following is conserved?

$A$ body of mass $m$ is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is (where $g$ is acceleration due to gravity at the surface of the earth).

The energy required to take a body from the surface of the earth to a height equal to the radius of the earth is $W$. The energy required to take this body from the surface of the earth to a height equal to twice the radius of the earth is:

An asteroid is moving directly towards the centre of the Earth. When at a distance of $10 R$ ($R$ is the radius of the Earth) from the Earth's centre,it has a speed of $12 \; km/s$. Neglecting the effect of Earth's atmosphere,what will be the speed of the asteroid when it hits the surface of the Earth? (Escape velocity from the Earth is $11.2 \; km/s$). Give your answer to the nearest integer in $km/s$.

$A$ body is thrown from the surface of the earth with velocity $V \ m/s$. The maximum height above the earth's surface up to which it will reach is ($R =$ radius of earth,$g =$ acceleration due to gravity).