A mass m hangs with help of a string wrapped around a pulley on a frictionless bearing. pulley has m

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6.System of Particles and Rotational Motion

hard

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

A

$\;\frac{3}{2}g$

B

$g$

C

$\;\frac{2}{3}g$

D

$\;\frac{g}{3}$

(AIEEE-2011)

Solution

For translational motion,

$mg – T = ma$ $ ….(1)$

For rotational motion,

$T.R = I$ $\alpha = I\frac{a}{R}$

Solving $(1) \& (2),$

$a = \frac{{mg}}{{\left( {m + \frac{I}{{{R^2}}}} \right)}} = \frac{{mg}}{{m + \frac{{m{R^2}}}{{2{R^2}}}}} = \frac{{2mg}}{{3m}} = \frac{{2g}}{3}$

Standard 11

Physics

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