Question

A uniform disc of mass $M$ and radius $R$ is mounted on an axle supported in friction less bearings. A light cord is wrapped around the rim of the disc and a steady downward pull $T$ is exerted on the cord. The angular acceleration of the disc is:

• A. $ \frac{MR}{2T} $
• B. $ \frac{2T}{MR} $
• C. $ \frac{T}{MR} $
• D. $ \frac{MR}{T} $

Answer 1

The Correct Option is B

The torque exerted on the disc is given by

$\tau=T R \ldots $(1) $\tau=I \alpha \ldots$(2) From eqs. (1) and (2), we get $I \alpha =T R $ $\alpha =\frac{T R}{I}$ or $ \alpha=\frac{2 T R}{M R^{2}}$ or $\alpha=\frac{2 T}{m R}$