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In the figure...

Question

In the figure shown a thin light inextensible string is wrapped around a uniform disc. One end of the string is fixed to the ceiling of the lift. Acceleration ' $a$ ' of the lift is such that the centre of disc does not move with respect to ground. Find the value of $\frac{a}{g} .$ String does not slip on pulley.

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Solution

$a_{A} = a = α . R$ ...(i)
$T - m g = 0$ ...(ii)
$T . R = \frac{m R^{2}}{2} . α$ ...(iii)
$∴ g = \frac{a}{2}$

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