A quantity \(x\) is given by \(\left( IF v^{2} / WL ^{4}\right)\) 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

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Answer & Solution

Correct Answer

(C) Energy density

Detailed explanation

\(x=\frac{I F V^{2}}{W L^{4}}\)

\([ x ]=\frac{\left[ ML ^{2}\right]\left[ MI T ^{-2}\right]\left[ L T ^{-1}\right]^{2}}{\left[ ML ^{2} T ^{-2}\right][ L ]^{4}}\)

\([ x ]=\left[ ML ^{-1} T ^{-2}\right]\)

[Energy density] \(=\left[\frac{ E }{ V }\right]\)

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

\(=\left[ ML ^{-1} T ^{-2}\right]\)

Same as \(x\)

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