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 $]=\left[\frac{F}{A} \times \frac{l}{\Delta l}\right]$
$=\frac{\left[M L T^{-2}\right]}{\left[L^{2}\right]} \frac{[L]}{[L]}=\left[M L^{-1} T^{-2}\right]$