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  4. Thread wound around a solid cylinder of mass M and radius R . It is allowed to fall as shown. Its acceleration is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-qzrusfbrr5bg9kk4.jpg />

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Q. Thread wound around a solid cylinder of mass $M$ and radius $R$ . It is allowed to fall as shown. Its acceleration is
Question

NTA AbhyasNTA Abhyas 2020

Solution:

$mg-T=ma...\left(\right.1\left.\right)$
$\tau=I\alpha $
$RT=\left(\frac{m R^{2}}{2}\right)\frac{a}{R}$
$T=\frac{m a}{2}...\left(2\right)$
Solving $\left(\right.1\left.\right)\&\left(\right.2\left.\right)$
$A=2g/3$