JEE MAIN - Physics (2014 (Offline) - No. 24)
A mass $$'m'$$ is supported by a massless string wound around a uniform hollow cylinder of mass $$m$$ and radius $$R.$$ If the string does not slip on the cylinder, with what acceleration will the mass fall or release?
_en_24_1.png)
$${{2g} \over 3}$$
$${{g} \over 2}$$
$${{5g} \over 6}$$
$$g$$
Explanation
_en_24_2.png)
Here string is not slipping over pulley.
From figure,
Acceleration $$a = R\alpha \,\,\,\,...(i)$$
Applying Newton's second law on the block we get,
$$mg-T=ma$$ $$...(ii)$$
Torque on cylinder due to tension in string about the fixed point,
$$T \times R = I\alpha$$
$$T \times R = m{R^2}\alpha = m{R^2}\left( {{a \over R}} \right)$$
[ as $$I$$ = MR2 for hollow cylinder]
or $$T=ma$$
$$ \Rightarrow \,\,mg - ma = ma$$
$$ \Rightarrow \,\,\,a = {g \over 2}$$
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