A uniform disc of mass $M$ and radius $R$ is released from the shown position. $P Q$ is a string, $O P$ is a horizontal line, $O$ is the centre of the disc and the distance $O P$ is $R / 2$ . Find the tension in the string just after the disc is released .

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Solution

$M a s s = M R a d i u s = R$
PQ is a string
OP is a horizontal line O
Applying Newton's law on centre of mass O
$M g - T = m g (a =$ acceleration os centre of mass)
$τ = I α$ (About centre of mass)
$T \times \frac{R}{2} = \frac{M R^{2}}{2} α A l s o, α = \frac{R}{2} a$
From equation $T = \frac{2 m g}{3}$

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