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A thin uniform rod of length l and mass ...

A thin uniform rod of length `l` and mass m is freely pivoted about its end. The rod is initially held horizontally and released from rest. When the rod is vertical, an impulse J is applied to bring it to rest (this is in addition to any impulse provided by the pivot)

The distance from the pivot at which impulse, must be applied, if there is to be no horizontal force at the pivot

A

`(l)/(2)`

B

`(l)/(3)`

C

`(2l)/(3)`

D

`l`

Text Solution

Verified by Experts

The correct Answer is:
C

(A) By applying COME
`"mg" (l)/(2)=(1)/(2)(ml^(2))/(3)omega^(2)`
`omega=sqrt((3g)/(l))`
(B) Impulse will be minimum if it is applied at lowest point
Angular impulse = Change in angular momentum
`Jxxl=I omega=(ml^(2))/(3)sqrt((3g)/(l))J=msqrt((gl)/(3))`
`J+J'=momega(l)/(2)=m(sqrt(3gl))/(2), J'=m(sqrt(gl))/(2 sqrt(3))`
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