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A uniform rod of length l is given an i...

A uniform rod of length `l` is given an impulse at right angles to its length as shown. Find the distance of instantaneous centre of rotation from the centre of the rod.
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Text Solution

Verified by Experts

The correct Answer is:
`(l^(2))/(12 x)`
For translational motion of `C.M`
`J = mv_(Cm), v_(Cm) = (J)/(m)`…(1)

rod will have rotational motion about `C.M`
`Jx = I omega, omega = (Jx)/(I)`…..(2)
`v_(CM) = y omega` …(3)
from (1),(2) & (3)
`(J)/(m) = y xx (Jx)/(I), y = (I)/(mx) rArr y = (l^(2))/(12 x)`.
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Knowledge Check

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