Question

A physical quantity $X$ is expressed as velocity $=\sqrt{\left(\frac{X}{\text{density}}\right)}$. 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 $\left[M{L}^{-1}{T}^{-2}\right]$

From the given expression
Velocity $=\sqrt{\left(\frac{X}{\text{density}}\right)}$,
we can say that
$\left[X\right]=\left[\right(\text{velocity}{)}^2\text{density}]$
$\Rightarrow \left[X\right]=\left[\right(L{T}^{-1}{)}^2\left(M{L}^{-3}\right)]=[M{L}^{-1}{T}^{-2}]$