Question

Among the following, the physical quantity having the dimensions of Young's modulus is
Identify the correct option from the following:

• A. strain
• B. gravitational potential
• C. surface energy
• D. energy density

Hint:

To compare physical quantities by dimensions, express each quantity in terms of fundamental units (mass, length, time) and match with the given quantity.

Answer 1

The Correct Option is D

Step 1: Determine the dimensions of Young's modulus
Young's modulus is stress divided by strain. Stress = force/area, dimensions: $[F]/[A] = [M L T^{-2}]/[L^2] = [M L^{-1} T^{-2}]$. Strain is dimensionless. Thus, Young's modulus has dimensions $[M L^{-1} T^{-2}]$. Step 2: Compare with the options
% Option (1) Strain: dimensionless, $[M^0 L^0 T^0]$.
% Option (2) Gravitational potential: energy/mass, $[E]/[M] = [M L^2 T^{-2}]/[M] = [L^2 T^{-2}]$.
% Option (3) Surface energy: energy/area, $[E]/[A] = [M L^2 T^{-2}]/[L^2] = [M T^{-2}]$.
% Option (4) Energy density: energy/volume, $[E]/[V] = [M L^2 T^{-2}]/[L^3] = [M L^{-1} T^{-2}]$, matches Young's modulus. Step 3: Select the correct option
Energy density has the same dimensions as Young's modulus, so the answer is (4).