Question

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. Then the acceleration of the body is :

• A. $\frac{2mg}{2m+M}$
• B. $\frac{2Mg}{2m+M}$
• C. $\frac{2Mg}{2M+m}$
• D. $\frac{2mg}{2M+m}$

Answer 1

The correct option is A $\frac{2mg}{2m+M}$

$T=I\alpha$

$F.R=I\alpha$

$mgR=(\frac{M{R}^2}{2}+m{R}^2)\alpha$

$2mgR=(2m+M)R^2\times \frac{a}{R}$

$a=\frac{2mg}{2m+M}$