$A$ particle of mass $M$ is placed at the centre of a uniform spherical shell of mass $2M$ and radius $R$. The gravitational potential on the surface of the shell is

$A$ body of mass $m$ rises to a height $h = R/5$ from the earth's surface,where $R$ is the earth's radius. If $g$ is the acceleration due to gravity at the earth's surface,the increase in potential energy is:

Calculate the energy needed to move a mass of $4 \, kg$ from the center of the Earth to its surface (in joules),given that the radius of the Earth is $6400 \, km$ and the acceleration due to gravity at the surface of the Earth is $g = 10 \, m/s^2$.

On the $x$-axis and at a distance $x$ from the origin,the gravitational field due to a mass distribution is given by $\frac{Ax}{(x^2+a^2)^{3/2}}$ in the $x$-direction. The magnitude of gravitational potential on the $x$-axis at a distance $x$,taking its value to be zero at infinity,is

The bodies of masses $100 \,kg$ and $8100 \,kg$ are held at a distance of $1 \,m$. The gravitational field at a point on the line joining them is zero. The gravitational potential at that point in $J/kg$ is $\left(G = 6.67 \times 10^{-11} \,Nm^2/kg^2\right)$

Objects of mass $m$ are placed on the $x$-axis at $x = 1, x = 2, x = 4, x = 8, \dots$ respectively. What is the gravitational potential at the origin $x = 0$?