Question

The power (P) is supplied to rotating body having moment of inertia 'I' and angular acceleration '\(α\)'. Its instantaneous angular velocity is

• A. \(\frac{I}{Pα}\)
• B. \(\frac{α}{PI}\)
• C. \(\frac{Pα}{I}\)
• D. \(\frac{P}{Iα}\)

Hint:

P = torque times omega and torque = I alpha.

Answer 1

The Correct Option is D

Step 1: Analogy:
Linear motion has $P=Fv$. The rotational version is $P=\tau\omega$.

Step 2: Use torque:
$\tau=I\alpha$ so $P=I\alpha\omega$.

Step 3: Dimension check:
$P$ is $ML^2T^{-3}$, $I$ is $ML^2$, $\alpha$ is $T^{-2}$. So $P/(I\alpha)=T^{-3}/T^{-2}=T^{-1}$, which is angular velocity. Option (D).

Final Answer:
Only P / (I alpha) has the unit of angular velocity. \[ \boxed{D} \]