Question

The dimensional formula of latent heat is identical to that of
A. Internal energy
B. Angular momentum
C. Gravitational potential
D. Electric potential

Answer 1

Hint: To give a solution to the given question, we must be thorough with the concept of the Dimensional formula which is a part of dimensional analysis.
Principally, dimensions of a physical quantity are the powers to which the base quantities or fundamental quantities are raised to represent the quantity and dimensional formula of physical quantity is a compound expression which shows how and which of the fundamental quantities are involved in making that physical quantity. For instance, the expression $\left[ {{M}^{0}}{{L}^{2}}{{T}^{0}} \right]$ is the dimensional formula for Area.

Complete step by step answer:
 Latent heat is basically the heat or thermal energy that is either absorbed or released during the phase transformation of a substance i.e. could be either from a gas to liquid or liquid to gas and vice versa.
Specific latent heat is generally categorized as the measure of warm vitality that is consumed or dissipated when a body experiences a steady temperature process and the formula for the same is given by:
$L=\dfrac{Q}{m}$
Where $L$ is the specific latent heat;
$Q$ Is the heat retained or dissipated;
$m$ is the mass of the substance.
I.e. specific latent heat has the dimension of Energy per unit mass and thus the dimensional formula of $\left[ {{M}^{0}}{{L}^{2}}{{T}^{-2}} \right]$and out of all the options given,
Only Gravitational potential is having the same dimension and dimensional formula of Energy per unit mass and $\left[ {{M}^{0}}{{L}^{2}}{{T}^{-2}} \right]$respectively, as Gravitational potential is the potential energy of a substance per unit mass.

So, the correct answer is “Option C”.

Note: One is advised to also look into the dimensions and dimensional formula of the other options given in the question,
Internal energy has units of energy and thus, dimensional formula of $\left[ {{M}^{1}}{{L}^{2}}{{T}^{-2}} \right]$
Angular momentum has the units of Joule per second and thus, dimensional formula of $\left[ {{M}^{0}}{{L}^{2}}{{T}^{-1}} \right]$
Electric potential has the units of energy per unit charge and thus, dimensional formula of$\left[ {{M}^{1}}{{L}^{2}}{{T}^{-3}}{{I}^{-1}} \right]$.