Question

A quantity $x$ is given by $\left(\frac{IF{v}^2}{W{L}^4}\right)$ in terms of moment of inertia $I$, force $F$, velocity $v$, work $W$ and Length $L$. The dimensional formula for $x$ is same as that of:

• A. Coefficient of viscosity
• B. Energy density
• C. Force constant
• D. Planck’s constant

Answer 1

The correct option is B

Energy density

Step 1. Given data

$x=\frac{IF{v}^2}{W{L}^4}$ in terms of moment of inertia $I$, force $F$, velocity $v$, work $W$ and Length $L$.

Step 2. Finding the dimensional formula of $x$

Where dimensions of all the terms are

Moment of inertia, $I$$=\left[M{L}^2\right]$

Force, $F$$=\left[ML{T}^{-2}\right]$

Velocity, $v$$=\left[L{T}^{-1}\right]$

Work, $W$$=\left[M{L}^2{T}^{-2}\right]$

Length, $L$ $=\left[L\right]$

On putting all the dimensions in given formulae, we get

$$\begin{gathered} x=\frac{IF{v}^2}{W{L}^4} \\ x=\frac{\left(M{L}^2\right)\left(ML{T}^{-2}\right){\left(L{T}^{-1}\right)}^2}{\left(M{L}^2{T}^{-2}\right)L^4} \\ x=M{L}^{-1}{T}^{-2} \end{gathered}$$

The dimensional formula for $x$ is same as that of Energy density.

Hence, option $\left(B\right)$ is correct.