Q. A circular disk of radius $R$ meter and mass $M$ kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that $\theta(t)=5t^2-8t$, where $\theta(t)$ is the angular position of the rotating disc as a function of time $t$. How much power is delivered by the applied torque, when $t=2$ s ?
A) $72MR^2$
B) $8MR^2$
C) $108MR^2$
D) $60MR^2$
Explanation
[Solution by Dr. Abubacker] $\omega=10t-8$ and $\alpha=10$ rad/s². $\tau=I\alpha=\frac{MR^2}2\cdot10=5MR^2$. At $t=2$: $\omega=12$, so $P=\tau\omega=60MR^2$. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.