Question

What is the SI unit of gravitational potential:
A. J
B. JKg-1
C. JKg
D. jKg-2

Answer 1

Hint: To solve this question we must know what is gravitational potential.
The amount of work done in moving a unit mass from infinity to some point in the gravitational field of a source mass is known as gravitational potential.
Simply, it is the gravitational potential energy possessed by a unit mass:
⇒ V = $\dfrac{U}{m}$
⇒ V = $ - \dfrac{{GM}}{r}$
Where, G is gravitational constant, M is the mass of the gravitational field source body and r is the distance between source mass and unit mass.

Complete step by step answer:
The gravitational potential at a point is nothing but the potential energy associated with a unit mass due to its position/configuration in the gravitational field of another body.
Also, the gravitational potential is defined as the amount of work done in bringing a body of unit mass from infinity to the point where potential has to be determined.
$\therefore $Gravitational potential (V) = $\dfrac{{{\text{work done in bringing the body from infinity}}}}{{{\text{mass of the body}}}} = \dfrac{{W\left( {joule} \right)}}{{m(Kg)}}$
SI unit of work (W) is Joule(J) and of mass is kilogram (Kg).
Therefore, the SI unit of gravitational potential is $\dfrac{J}{{Kg}} = JK{g^{ - 1}}$ .

So, the correct answer is “Option B”.

Additional Information:
The gravitational potential at a point is nothing but the potential energy associated with a unit mass due to its position/configuration in the gravitational field of another body.
Also, the gravitational potential is defined as the amount of work done in bringing a body of unit mass from infinity to the point where potential has to be determined.
$\therefore $Gravitational potential (V) = $\dfrac{{{\text{work done in bringing the body from infinity}}}}{{{\text{mass of the body}}}} = \dfrac{{W\left( {joule} \right)}}{{m(Kg)}}$
SI unit of work (W) is Joule(J) and mass is kilogram (Kg).
Therefore, the SI unit of gravitational potential is $\dfrac{J}{{Kg}} = JK{g^{ - 1}}$ .

Note:
The gravitational potential at a point is always taken negative and potential (V) is maximum at infinity.
The dimensional formula of gravitational potential is:\[{M^0}{L^2}{T^{ - 2}}\].