Question

A uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. A string 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:

Answer 1

$mg-T=ma$

$RT=K$

$RT=\frac{{MR}^2}{2}\frac{a}{R}$

$T=\frac{Ma}{2}$

$mg-\frac{Ma}{2}=ma$

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

$mg=a\left(\frac{M+2m}{2}\right)$

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