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

The Correct Option is D

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