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A uniform rod of maass m and length L is...

A uniform rod of maass `m` and length `L` is placed on the fixed cylindrical surface of radius `R` at an small angular position `theta` from the vertical (vertical means line joining centre and vertex of the cylindrical path) as shown in the figure and released from rest. Find the angular velocity `omega` of the rod at the instant when it crosses the horizontal position (Assume that when rod comes at horizontal position its mid point and vertex of the circular surface coincide). Friction is sufficient to prevent any slipping.

Text Solution

Verified by Experts

Gain in kinetic energy `=` loss in potential energy
`(1)/(2)(ml^(2))/(12)omega^(2)=mgR[theta sintheta+costheta-1]`
`omega=(2)/(l)sqrt(6gR(theta sintheta+costheta-1))`
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