Question

The dimensional representation of gravitational potential is identical to that of
(A) Internal energy
(B) Angular momentum
(C) Latent heat
(D) Electric potential

Answer 1

Hint
From Encyclopedia of Mathematics. A linear representation of a topological group in a finite-dimensional vector space. The theory of finite-dimensional representations is one of the most important and most developed parts of the representation theory of groups.

Complete step by step answer
Dimension of gravitational potential is derived as follows.
Gravitational potential energy = mass * acceleration due to gravity * altitude...........equation1
Dimension formula for
Mass =$[{M^1}{L^0}{T^0}]$ and altitude is $[{M^0}{L^1}{T^0}]$
Where M= mass, L= length,T=time
G =$[{M^0}{L^1}{T^2}]$
Substitute every single terms of the main equation 1
G.P.E = $[{M^1}{L^2}{T^2}]$
Latent heat is heat absorbed or released per unit mass of the substance at its melting point into liquid of some temperature.
Latent heat(L) = heat/mass
Dimensional formula of heat(Q) = $[{M^0}{L^1}{T^{ - 2}}]$
Formula for mass = $[{M^1}{L^0}{T^0}]$
Now, substituting the values
L = $\dfrac{{[{M^1}{L^2}{T^{ - 2}}]}}{{[{M^1}{L^0}{T^0}]}}$
L= $[{M^0}{L^2}{T^{ - 2}}]$
So, The dimensional representation of gravitational potential is identical to that of latent heat.
Correct option is (C) .

Note
Latent heat is the heat required to convert a solid into a liquid or vapour, or a liquid into a vapour, without change of temperature.