Question

A uniform disc of mass $M$ and radius $R$ is released from rest in the shown position. $PQ$ is a string, $OP$ is a horizontal line, $O$ is the centre of the disc and distance $OP$ is $\frac{R}{2}$. Then tension in the string just after the disc is released will be:

• A. $\frac{Mg}{2}$
• B. $\frac{Mg}{3}$
• C. $\frac{2Mg}{3}$
• D. none of these

Answer 1

The correct option is A $\frac{Mg}{2}$

Applying Newton's law on centre of mass O
$Mg-T=Ma$
{ a=acceleration of centre of mass}
$\tau =I\alpha$, about centre of mass
$T\frac{R}{2}=\frac{M{R}^{{}^2}}{2}.\alpha$
or
$M(g-a)\frac{R}{2}=\frac{M{R}^{{}^2}}{2}.\frac{a}{R}$
Solving we get
$a=\frac{g}{2}$
from above equations
$T=\frac{Mg}{2}$