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 $\frac{2T}{MR}$

$\because \overrightarrow{\tau }=\overrightarrow{R}\times \overrightarrow{F}$
$\Rightarrow \tau =RFsin\theta$
Here, $F=T$ (downward pull) and $\theta ={90}^o$
$\therefore \tau =RT$
Also $\tau =1\alpha$
$\therefore I\alpha =TR$
For a disc. $I=\frac{M{R}^2}{2}$
$\therefore TR=\frac{M{R}^2}{2}.\alpha$
$\Rightarrow \alpha =\frac{2T}{MR}$