A quantity $x$ is given by


A quantity $x$ is given by $\left(I F v^{2} / W L^{4}\right)$ 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:

  1. planck's constant

  2. force constant

  3. energy density

  4. coefficient of viscosity

Correct Option: , 3


(3) Dimension of Force $F=\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}$

Dimension of velocity $V=\mathrm{L}^{1} \mathrm{~T}^{-1}$

Dimension of work $=\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}$

Dimension of length $=\mathrm{L}$

Moment of inertia $=\mathrm{ML}^{2}$

$\therefore x=\frac{I F v^{2}}{W L^{4}}$

$=\frac{\left(M^{1} L^{2}\right)\left(M^{1} L^{1} T^{-2}\right)\left(L^{1} T^{-2}\right)^{2}}{\left(M^{1} L^{2} T^{-2}\right)\left(L^{4}\right)}$

$=\frac{\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-2}}{\mathrm{~L}^{3}}=\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}=$ Energy density

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