Question

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 :

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

Answer 1

The Correct Option is C

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