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A uniform rod smoothly pivoted at one of...

A uniform rod smoothly pivoted at one of its ends is released from rest. If it swings in vertical plane, the maximum speed of the end `P` of the rod is.
.

A

`2 sqrt(3 g l)`

B

`sqrt(3 g l)`

C

`2 sqrt(2 g l)`

D

`sqrt(g l)`

Text Solution

Verified by Experts

The correct Answer is:
B
(b) At the time of maximum speed of point `P`. The rod should be vertical
`Delta K + Delta U = 0`
`[(1)/(2) ((m l^2)/(3)) omega^2 - 0]+[- mg ((l)/(2))] = 0 rArr omega = sqrt((3g)/(l))`
Velocity of point `P V_P = omega l = sqrt(3 g l)`.
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