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 Option 1) $\frac{3}{2}g$ Option 2) $g$ Option 3) $\frac{2}{3}g$ Option 4) $\frac{g}{3}$

As we learnt in

Rolling of a body on an inclined plane -

$a= \frac{g\sin \Theta }{1+\frac{K^{2}}{R^{2}}}$

$f= \frac{mg\sin \Theta }{1+\frac{R^{2}}{K^{2}}}$

- wherein

$\Theta$ = Angle of inclination

$a=\frac{Mg}{m+\frac{I}{R^{2}}}=\frac{Mg}{m+\frac{1}{2}\frac{mR^{2}}{R^{2}}}$

$a=\frac{2Mg}{3m}$

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

Option 1)

$\frac{3}{2}g$

This is an incorrect option.

Option 2)

$g$

This is an incorrect option.

Option 3)

$\frac{2}{3}g$

This is the correct option.

Option 4)

$\frac{g}{3}$

This is an incorrect option.

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