Question 346: Centre of Mass and Rotational Motion

Question

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?

Accepted Answer

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,
$$T 	imes R = I\alpha$$
$$T 	imes R = m{R^2}\alpha  = m{R^2}\left( {{a \over R}} ight)$$
[ as $$I$$ = MR
2
for hollow cylinder]
or $$T=ma$$
$$ \Rightarrow \,\,mg - ma = ma$$
$$ \Rightarrow \,\,\,a = {g \over 2}$$

Answer

$${{2g} \over 3}$$

Answer

$${{g} \over 2}$$

Answer

$${{5g} \over 6}$$

Answer

$$g$$

Centre of Mass and Rotational Motion

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?

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