A uniform rod of length `l` is from rest such that it rotates about a smooth pivot. The angular speed of the rod when it becomes vertical is.
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Options

A. `2 sqrt((6 g)/(7 l))`
B. `sqrt((6 g)/(7 l))`
C. `2 sqrt((3 g)/(7 l))`
D. ` sqrt((3 g)/(7 l))`

Answer

A

Explanation

(a) `Delta K + Delta U = 0`
`((1)/(2)I_0 omega^2 - 0)+[- mg ((l)/(4))] = 0` …(i)
`I_0 = (m l^2)/(12) + m((l)/(4))^2 = (7)/(48) ml^2` …(ii)
From (i) and (ii), `omega = 2 sqrt((6 g)/(7 l))`.
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