Question

The SI unit of gravitational potential is
(A) $J$
(B) $J\;k{g^{ - 1}}$
(C) $J\;kg$
(D) $J\;k{g^{ - 2}}$

Answer 1

Hint
The gravitational potential will depend on the mass and the gravitational potential energy. The SI units of those depending factors have to be found and finally the SI unit of gravitational potential can be found.

Complete step by step answer
The gravitational potential can be considered as the electric potential in the electrostatics which relates to bringing a charge from infinity to a point. And the gravitational potential can be called the Newtonian potential. This can be used in general relativity and electrostatics and magnetostatics of the large bodies in space.
We know about the expression for the gravitational potential. It is given as
$\Rightarrow V = \dfrac{U}{m}$
Where, $U$ is the potential energy and $m$ is the mass.
The gravitational potential can be defined as the potential energy at that point per unit mass.
And we know that the potential energy is the equal in magnitude of the work done for bringing a mass from infinity to that point. And the SI unit of the work done or the energy is Joules $\left( J \right)$ .
And the SI unit of the mass is kilogram$\left( {kg} \right)$. Thus the SI unit of gravitational energy when substituting on the above expression will give as,
$\Rightarrow \dfrac{J}{{kg}}$
Hence the SI unit of gravitational potential is $J\;k{g^{ - 1}}$.
The answer is option (B).

Note
We want to note that the gravitational potential will be equal to the gravitational potential energy if the mass is unit mass. That is for one kilogram mass, the work done to bring that mass will be gravitational potential.