Q.

A thin rod has a non-uniform density. It is mounted on an axle passing perpendicular to it, through its center of mass, as shown, and is then rotated about the axle.
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The axle divides the rod into two parts, one on each side of it. Which of the following must be true, no matter how the mass in the rod is distributed?
 

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a

The magnitudes of the angular momentum of the two parts, about the center of mass, are equal.

b

The two parts have the same mass.

c

The magnitudes of the momentum of the two parts are equal.

d

The kinetic energies of the two parts are equal.

answer is B.

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A thin rod has a non-uniform density. It is mounted on an axle passing perpendicular to it, through its center of mass, as shown, and is then rotated about the axle.The axle divides the rod into two parts, one on each side of it. Which of the following must be true, no matter how the mass in the rod is distributed?