A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass

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6.System of Particles and Rotational Motion

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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 on release?

A

$\frac{g}{2}$

B

$g$

C

$\;\frac{{5g}}{6}$

D

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

(JEE MAIN-2014)

Solution

From figure, Acceleration

$a=R\alpha $ . . . (i)

and $mg-T=ma$ . . .(ii)

From equation (i) and (ii)

$T \times R = m{R^a} = m{R^2}\left( {\frac{a}{R}} \right)$

$T=ma$

$mg-ma=ma$

$a=g/2$

Standard 11

Physics

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