Q119 / 150 · MHT CET 2026 (15 April Shift 1) · Physics
The power (P) is supplied to rotating body having moment of inertia 'I' and angular acceleration '$\alpha$'. Its instantaneous angular velocity is
- A$\dfrac{I}{P\alpha}$
- B$\dfrac{\alpha}{PI}$
- C$\dfrac{P\alpha}{I}$
- Correct answerD$\dfrac{P}{I\alpha}$
Solution
Power $P$ supplied to a rotating body is given by the product of torque $\tau$ and angular velocity $\omega$.
$P = \tau \omega$
The torque $\tau$ acting on the body is related to its moment of inertia $I$ and angular acceleration $\alpha$ by the relation:
$\tau = I \alpha$
Substituting the value of $\tau$ in the power equation:
$P = (I \alpha) \omega$
Rearranging for instantaneous angular velocity $\omega$:
$\omega = \dfrac{P}{I \alpha}$
Answer: $\dfrac{P}{I\alpha}$
$P = \tau \omega$
The torque $\tau$ acting on the body is related to its moment of inertia $I$ and angular acceleration $\alpha$ by the relation:
$\tau = I \alpha$
Substituting the value of $\tau$ in the power equation:
$P = (I \alpha) \omega$
Rearranging for instantaneous angular velocity $\omega$:
$\omega = \dfrac{P}{I \alpha}$
Answer: $\dfrac{P}{I\alpha}$
Hence, the correct answer is option: 'D'.