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 pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is :

Engineering

Physics

Pure Rotational Motion

Question

$\frac{3}{2} g$

$\frac{g}{3}$

$\frac{2}{3} g$

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mg – T = ma

$TR = \frac{{mR}^{2} α}{2}$

$T = \frac{mRα}{2} = \frac{ma}{2}$

$mg - \frac{ma}{2} = ma$

$\frac{3 ma}{2} = mg$

$a = \frac{2 g}{3}$