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A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming the pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

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$\frac{2}{3} g$

$\frac{3}{2} g$

$\frac{g}{3}$

answer is B.

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Detailed Solution

For the mass, m:

$mg - T = ma$ .......(1)

The pulley experiences a torque. If $α$ is its angular acceleration, then

$τ = TR = Iα$

$Now, I = \frac{1}{2} {MR}^{2} and α = \frac{a}{R}, therefore,$

$TR = (\frac{1}{2} {MR}^{2}) \frac{a}{R} \Rightarrow T = \frac{1}{2} Ma$

$substituting in Eq . (1),$

$mg - \frac{1}{2} ma = ma \Rightarrow a = \frac{2 g}{3}$

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