$A$ body is projected vertically upwards from the Earth's surface of radius $R$ with a velocity equal to $\frac{1}{3}$ of the escape velocity. The maximum height reached by the body is

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 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).

$A$ body is projected vertically upwards from the earth's surface. If its kinetic energy of projection is equal to half of its minimum value required to escape from the gravitational influence,then the height up to which it rises is ($R =$ radius of the earth).

Two masses $m_1$ and $m_2$ are at rest at infinity. Find their relative velocity of approach due to gravitational attraction when their separation is $d$.

$A$ body of mass $m$ is taken from the earth's surface to a height equal to twice the radius $(R)$ of the earth. The change in potential energy of the body will be