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  4. A quantity x is given by (IFv2 / WL4) 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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Q. A quantity $x$ is given by $(IFv^2 / WL^{4})$ 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 :

JEE MainJEE Main 2020Physical World, Units and Measurements

Solution:

$x =\frac{ IFV ^{2}}{ WL ^{4}}$
$[ x ]=\frac{\left[ ML ^{2}\right]\left[ MLT ^{-2}\right]\left[ LT ^{-1}\right]^{2}}{\left[ ML ^{2} T ^{-2}\right][ L ]^{4}}$
$[ x ]=\left[ ML ^{-1} T ^{-2}\right]$
[Energy density] $=\left[\frac{ E }{ V }\right]$
$=\left[\frac{ ML ^{2} T ^{-2}}{ L ^{3}}\right]$
$=\left[ ML ^{-1} T ^{-2}\right]$
Same as $x$