Question

The dimension of mass is zero in which of the following physical quantities?
(A) Gravitational potential
(B) Latent heat
(C) Specific heat capacity
(D) All of the above

Answer 1

Hint
The gravitational potential at a point in a gravitational field is the work done per unit mass that would have to be done by some externally applied force to bring a massive object to that point from some defined position of zero potential, usually infinity .

Complete step by step answer
The dimension of the gravitational potential = $ [\dfrac{{Force}}{{Mass}} \times r] = [\dfrac{{{M^1}{L^2}{T^{ - 2}}}}{{{M^1}}}] = [{M^0}{L^2}{T^{ - 2}}] $ ......(1)
Now, the latent heat is an energy absorbed or released by a substance during a change in its physical state (phase) that occurs without changing its temperature.
Dimension of the latent heat is, = $ [\dfrac{{Energy}}{{Mass}}] = [\dfrac{{{M^1}{L^2}{T^{ - 2}}}}{M}] = [{L^2}{T^{ - 2}}] $ ......(2)
Now, the dimension of the specific heat capacity is = $ [\dfrac{{Energy}}{{Mass \times temp}}] = [\dfrac{{{M^1}{L^2}{T^{ - 2}}}}{{{M^1}{K^1}}}] = [{L^2}{T^{ - 2}}{K^{ - 1}}] $ .....(3)
So, the dimension of mass is zero in every physical quantity in the option.

Note
The heat capacity and the specific heat are related by $C=cm$ or $c=C/m$. The mass $m$, specific heat $c$, change in temperature $ΔT$, and heat added (or subtracted) $Q$ are related by the equation: $Q=mcΔT$. Values of specific heat are dependent on the properties and phase of a given substance.