In a gravitational field,at a point where the gravitational potential is zero,

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

If the mass of the Earth is $M$,its radius is $R$,and the gravitational constant is $G$,then the work done to take a $1 \, kg$ mass from the Earth's surface to infinity will be:

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

If the potential at the surface of the Earth is assigned a zero value,then the potential at the center of the Earth will be (Mass $= M$,Radius $= R$).

If the gravitational potential energy of two point masses infinitely away is taken to be zero,then the gravitational potential energy of a galaxy is ...............