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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
Change in angular momentum of the system = angular impulse given to the system `=("angular momentum")_(f) -("angular momentum")_(I)`
`=MV xx L/2`………(i)
Let the system starts rotating with angular velocity `omega`.
Moment of inertia of the system about its axis rotation (centre of mass of the system).
`=M(L/2)^(2) + M(L/2)^(2) = (2ML^(2))/4 = (ML^(2))/2` From (i)
`I omega -0 = MV xx L/2 rArr omega = (MV)/IO xx L/2 = (MV)/(ML^(2)//2) xx L/2 = V/L`.
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