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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Options

A. `2tan^(-1)2`
B. `tan^(-1)2`
C. `tan^(-1)1`
D. `tan^(-1)4`

Answer

A

Explanation

`W_("all forces")=DeltaKE`
`-mgR(1-cos theta)+(m)(2g)R sin theta=0`
`mgR[-2 sin^(2).(theta)/(2)+(2)sin theta]=0`
`sin theta=sin^(2)((theta)/(2))`
`2sin.(theta)/(2)cos.(theta)/(2)=(sin theta)/(2).(sin theta)/(2)`
`2=tan.(theta)/(2) rArr theta=2(tan^(-1)2)`