# A quantity x is given by $(IFv^{2}/WL^{4})$ in terms of a moment of interia I, force F, velocity v, work W and length L. the dimensional formula for the x is same as that of: Option: 1 planck's constant Option: 2 force constant Option: 3 Energy density Option: 4 coefficient of viscosity

\begin{aligned} &\begin{array}{l} \mathrm{x}=\frac{\mathrm{IFV}^{2}}{\mathrm{WL}^{4}} \\ \\ {[\mathrm{x}]=\frac{\left[\mathrm{ML}^{2}\right]\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{LT}^{-1}\right]^{2}}{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right][\mathrm{L}]^{4}}} \\\\ {[\mathrm{x}]=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]} \\\\ \text {[Energy density] }=\left[\frac{\mathrm{E}}{\mathrm{V}}\right] \\\\ =\left[\frac{\mathrm{ML}^{2} \mathrm{~T}^{-2}}{\mathrm{~L}^{3}}\right] \\\\ =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right] \end{array}\\ \\ &\text { Same as } x \end{aligned}

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