Question

A physical quantity $X$ is expressed as velocity$=\sqrt{\frac{X}{density}}$ . The dimensions of $X$ are

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

Answer 1

The correct option is C $\left[M{L}^{-1}{T}^{-2}\right]$

We are given that that $Velocity=\sqrt{\frac{X}{Density}}$

Writing the equation in terms of dimension, we have

$\left[L{T}^{-1}\right]=\sqrt{\frac{X}{\frac{\left[M\right]}{\left[L^3\right]}}}$

$\left[L^2{T}^{-2}\right]=\frac{\left[X{L}^3\right]}{\left[M\right]}$

The dimension of $X=\left[M{L}^{-1}{T}^{-2}\right]$