Q. Rotational kinetic energy of a body is given by the equation $E=\frac{I \omega^{2}}{2}$ where $I$ is moment of inertia and $w$ angular velocity of the body. The dimensional formula of I using the above equation is

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A

$ML ^{2} T ^{0}$

B

$ML ^{2} T ^{1}$

C

$M ^{2} L ^{1} T ^{1}$

D

$MLT$

Solution:

$E =\frac{ I \omega^{2}}{2}$
$ I=\frac{2 E}{\omega^{2}}=\frac{M L^{2} T^{-2}}{T^{-1^{2}}}= ML ^{2}\, T ^{0}$

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