Question

The SI unit of gravitational potential is :
(A) $Joule/kg$
(B) $Joule^2 /kg$
(C) $kg/Joule$
(D) $Joule/kg^2$

Answer 1

Hint
The S.l. system of unit measurement is the international system of measurement of units. The SI unit of the measurement is accepted world-wide. The Sl system is formed to make the communication easy world-wide.

Complete step by step solution
The gravitational force of attraction between any two objects is:
Directly proportional to the product of masses and Inversely proportional to the square of distance between them. The gravitational force of attraction is given by,
$F = \dfrac{{\mathop {Gm}\nolimits_1 \mathop m\nolimits_2 }}{{\mathop r\nolimits^2 }}$
Where, G is the gravitational constant, $\mathop m\nolimits_1$ and $\mathop m\nolimits_2$ are the masses of the objects and r is the distance between the objects
We should know that gravitational potential is defined as the work done in bringing a unit mass from infinity to the point of interest. So gravitational potential is work done on a unit mass.
$Gravitational{\text{ }}Potential = \dfrac{{Work{\text{ }}Done}}{{Mass}}$
$\left( {SI{\text{ }}unit{\text{ }}of{\text{ }}Gravitational{\text{ }}Potential} \right){\text{ }} = {\text{ }}\dfrac{{\left( {SI{\text{ }}unit{\text{ }}of{\text{ }}Work{\text{ }}Done} \right)}}{{\left( {SI{\text{ }}unit{\text{ }}Of{\text{ }}Mass} \right)}}{\text{ }}$
As we know that
$SI{\text{ }}unit{\text{ }}of{\text{ }}Work{\text{ }}Done{\text{ }} = {\text{ }}Joule$
$SI{\text{ }}unit{\text{ }}of{\text{ }}mass{\text{ }} = {\text{ }}Kg$
Now put the SI units of Work Done and Mass in the gravitational Potential Equation-
${\text{SI unit of Gravitational Potential }} = {\text{ }}\dfrac{{Joule}}{{Kg}}{\text{ }}$
${\text{SI unit of Gravitational Potential }} = {\text{ Joule/kg}}$
Thus option (A) is correct.

Note
The work required in bringing an object from infinity to a point in the presence of the gravitational field is known as the gravitational potential energy. It is represented by U that is $U = mgh$, where m is the mass, g is the acceleration due to the gravity, h is the height