Question

Energy per unit volume u is given by the relation $u=\frac{a}{b}cos\left(\frac{az}{k\theta }\right)$ where z is distance, k is Boltzmann constant, $\theta$ is temperature. Then the dimensional formula of b is

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

Answer 1

The correct option is B $\left[M^0{L}^2{T}^0\right]$

$\frac{az}{k\theta }$ is dimensionless
$\left[a\right]=\left[\frac{k\theta }{z}\right]=\left[ML{T}^{-2}\right]\therefore \left[b\right]=\left[\frac{a}{u}\right]=\left[\frac{ML{T}^{-2}}{M{L}^{-1}{T}^{-2}}\right]=\left[M^0{L}^2{T}^0\right]$