Question 183 of 280

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$\dfrac{2\text{g}}{3}$B$\dfrac{\text{g}}{2}$C$\dfrac{5\text{g}}{6}$D$\text{g}$

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Answer: (B) $\dfrac{\text{g}}{2}$

mg - T = ma ----- 1

$TR = I\alpha$

$TR={mR}^{2}\alpha$

​$∴T=mR\alpha$ ----2

For no slippping

a = Rα ---3

putting (3) in (2)

T = ma ---4

Adding 1 and 4

mg = 2ma

$∴a=\dfrac{g}{2}$