Question

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

• A. $ML ^{2} T ^{0}$
• B. $ML ^{2} T ^{1}$
• C. $M ^{2} L ^{1} T ^{1}$
• D. $MLT$

Answer 1

Answer: (A)

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