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A circular cylinder has an inextensible ...

A circular cylinder has an inextensible string wrapped around it as shown in figure. What is the linear acceleration of the cylinder when released?

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Let F be the tension in the strong. If a is the acceleration of the CM of the cylinder.
mg-F = ma………(i)
If `omega` is the torqed produced by the force about the axis of the cylinder through O, (i.e., CM of the cylinder), then
`omega =rF`
As `F =(1alpha)/r = (1/2 mr^(2))a/r (as I=(1//2) mr^(2))` or
`F=1/2 m r alpha = 1/2 ma` (as `a = ralpha`)
From eqn. (i), `mg -1/2 ma = ma` or `mg =3/2 m.a` or `a=2/3 g`
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