Question

Which two of the following five physical parameters have the same dimensions?
(A) Energy density
(B) Refractive index
(C) Dielectric constant
(D) Young’s modulus
(E) Magnetic field

• A. (B) and (D)
• B. (C) and (E)
• C. (A) and (D)
• D. (A) and (E)

Answer 1

Answer: (C)

$[$ Energy density $]=\frac{[\text{ Work done }]}{[\text{ Volume }]}$
$=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^3\right]}=\left[M{L}^{-1}{T}^{-2}\right]$
$[$ Young's modulus $]=\left[\frac{F}{A}\times \frac{l}{\Delta l}\right]$
$=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}\frac{[L]}{[L]}=\left[M{L}^{-1}{T}^{-2}\right]$