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String is wrapped over a pulley and free...

String is wrapped over a pulley and free end is fixed to the ceiling as shown in figure. Mass of the pulley is m and its radius is R. Assume that pulley is identical to dise. Calculate acceleration of pulley as it is allowed to fall by unwinding the string. Assume that string does not slip over the pulley.

Text Solution

Verified by Experts

Forces acting on the pulley are as shown in figure. Let a be the acceleration of the pulley and we know that string is not slipping over the pulley hence we can assume that angular acceleration. `alpha=a//R`
Using F - ma in the vertical direction we can write the following:
`mg-T =ma" "...(1)`
Using `tau=I alpha` about the centre of pulley we can write the following:
`mg-(ma)/(2)= ma rArr g=(3)/(2) a rArr a=(2g)/(3)`
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