A mass M hangs on a massless rod of length l which rotates at a...

A mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass $M$ moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity $ω .$ The angular momentum of $M$ about point $A$ is ${L}_{A}$ which lies in the positive $z$ direction and the angular momentum of $M$ about $B$ is ${L}_{B} .$ The correct statement for this system is:

A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with

Options

A ${L}_{A}$ and ${L}_{B}$ are both constant in magnitude and direction
B ${L}_{B}$ is constant in direction with varying magnitude
C ${L}_{B}$ is constant, both in magnitude and direction
D ${L}_{A}$ is constant, both in magnitude and direction

Correct answer

D. ${L}_{A}$ is constant, both in magnitude and direction

Step-by-step solution

We know, $\overset{\to}{L} = m ( \overset{\to}{r} \times \overset{\to}{v} )$

Now with respect to $A,$ we always get direction
of $\overset{\to}{L}$ along $+ ve$ $z$ -axis and also constant magnitude as mvr. But with respect to $B,$ we get constant magnitude but continuously changing direction.

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