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1.Units, Dimensions and Measurement
hard
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
A
Planck's constant
B
Force constant
C
Energy density
D
Coefficient of viscosity
(JEE MAIN-2020)
Solution
$x=\frac{I F V^{2}}{W L^{4}}$
$[ x ]=\frac{\left[ ML ^{2}\right]\left[ MI T ^{-2}\right]\left[ L T ^{-1}\right]^{2}}{\left[ ML ^{2} T ^{-2}\right][ L ]^{4}}$
$[ x ]=\left[ ML ^{-1} T ^{-2}\right]$
[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 $x$
Standard 11
Physics
