Question

An expression of energy density is given by
$u = \frac{α}{β} sin (\frac{αx}{kt})$
, where α, β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be

• A. $[ML^2T^{-2}θ^{-1}]$
• B. $[M^0L^2T^{-2}]$
• C. $[M^0L^0T^0]$
• D. $[M^0L^2T^0]$

Answer 1

Answer: (D)

$[M^0L^2T^0]$

Answer 2

The correct answer is (D) : $[M^0L^2T^0]$
$u = \frac{α}{β} sin (\frac{αx}{kt})$
$[α] = [\frac{kt}{x}] = \frac{[Energy]}{[Distance]}$
$[β] = \frac{[α]}{[u]}$
$= \frac{[Energy]/[Distance]}{[Energy]/[Volume]}$
$= [L^2]$