MC 14 Two straight metal rods with equal lengths but differing masses are firmly

Question

MC 14 Two straight metal rods with equal lengths but differing masses are firmly welded together at their centers of mass so that they make an angle 6, as in the diagram to the right. The mass of one of the rods is uniformly-distributed along its length, while the other has a non-uniform mass distribution. If this rigid object is now rotated around one of the points A or B at some fixed rotational speed co, around which point will the object have the most kinetic energy? a. A b. B c. It could be either A or B, depending upon which rod has more mass d. It could be either A or B, depending upon the value of 6 assuming it can be anything from 0° to 180°). e. Both (c) and (d) are true.

Explanation / Answer

as KE = 1/2 I

as angular velocity is same for both so I will be decision factor

case - 1 when the systen is roteted about A

I = Ia + Ib

I = ma L2/3 + [ Icom + mbd2 ]

case -2 when system is rotating about B

I = mbL2/3 + [ Icom + mad2 ]

as we can see in both case it is depend on the position of center of mass and distance d

which means depends on the which has more mass and the angle b/w them

so

answer is e

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