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A block of mass m is placed inside a smo...

A block of mass `m` is placed inside a smooth hollow cylinder of radius `R` kept horizontally. Initially system was at rest. Now cylinder is given constant acceleration `2 g` in the horizontal direction by external agent. Find the maximum angular displacement of the block with the vertical.
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Text Solution

Verified by Experts

The correct Answer is:
`2 tan^(-1) (2)`.
Free body diagram is :

`N cos theta = mg`
`N sin theta = m (2g)`
`rArr tan theta = 2`
`rArr theta = tan^(-1) (2)`
`:.` Maximum possible angular dispalcement
`= 2 theta`
`= 2 tan^(-1) (2)`.
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