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

Two uniform solid spheres of equal radii $R$,but mass $M$ and $4M$ have a centre-to-centre separation $6R$,as shown in the figure. The two spheres are held fixed. $A$ projectile of mass $m$ is projected from the surface of the sphere of mass $M$ directly towards the centre of the second sphere. Obtain an expression for the minimum speed $v$ of the projectile so that it reaches the surface of the second sphere.

Suppose two planets (spherical in shape) of radii $R$ and $2R$,but mass $M$ and $9M$ respectively have a centre-to-centre separation $8R$ as shown in the figure. $A$ satellite of mass $m$ is projected from the surface of the planet of mass $M$ directly towards the centre of the second planet. The minimum speed $v$ required for the satellite to reach the surface of the second planet is $\sqrt{\frac{a}{7} \frac{GM}{R}}$,then the value of $a$ is $....$
[Given: The two planets are fixed in their position]

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

$A$ stationary object is released from a point $P$ at a distance $3R$ from the centre of the moon,which has radius $R$ and mass $M$. Which of the following gives the speed of the object on hitting the moon?

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 $R = 6400 \, km$].