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
(a) Change in angular momentum of the system = angular impulse given to the system about the centre of mass `(Angular momentum)_f - (Angular momentum)_i` `= Mvxx(L)/(2)……(i)` Let the system starts rotating with the angular velocity `omega.` Moment of inertia of the system about its axis of rotation [centre of mass of the system] `=M((L)/(2))^2 +M((L)/(2)^2 = (2ML^2)/(4) = (ML)^2/(2)` From (i) `Iomega-O = Mv(L)/(2)` `rArr omega = (Mv)/(I)xx(L)/(2) = (Mv)/(ML^2/2)xx(L)/(2) = (v)/(L).`
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