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Consider a body, shown in figure, consis...

Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J = MV is imparted to the body at one of its ends what would be it angular velocity?

A

`v//L`

B

`2v//L`

C

`v//3L`

D

`v//4L`

Text Solution

Verified by Experts

The correct Answer is:
A
Initial angular momentum of the system about point O
= Linear momentum `×` Perpendicular distance of linear momentum from the axis of rotation =`Mv((L)/(2))…(i)`
Final angular momentum of the system about point `O=I_(1)omega+I_(2)omega=(I_(1)+I_(2))omega=[M((L)/(2))^(2)+M((L)/(2))^(2)]omega...(ii)`
Applying the law of conservation of angular momentum
`implies Mv((L)/(2))=2M((L)/(2))^(2)omega`
`implies omega=(v)/(L)`
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