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Question

Two small balls A and B, each of mass m, are attached rigidly to the ends of a light rod of length d. The structure rotates about the perpendicular bisector of the rod at an angular speed ω. The angular momentum of the system about the axis of rotation is .

A
mωd2
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B
2mωd2
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C
12mωd2
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D
14mωd2
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Solution

The correct option is C 12mωd2

Consider the situation shown in figure. The magnitude of the velocity of the ball A with respect to the centre O is v=ωd2.
The angular momentum of the ball with respect to the axis is L1=mvr=m(ωd2)(d2)=14mωd2.

The same is the angular momentum L2 of the second ball. The angular momentum of the system is equal to sum of these two angular momenta i.e., L=12 mωd2.


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