A mass M hangs on a massless

Question:

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 $\omega$. 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 :

  1. $\mathrm{L}_{\mathrm{A}}$ and $\mathrm{L}_{\mathrm{B}}$ are both constant in magnitude and direction

  2. $\mathrm{L}_{\mathrm{B}}$ is constant in direction with varying magnitude

  3. $L_{B}$ is constant, both in magnitude and direction

  4. $\mathrm{L}_{\mathrm{A}}$ is constant, both in magnitude and direction

Correct Option: , 4

Solution:

We know, $\overrightarrow{\mathrm{L}}=\mathrm{m}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{V}})$

Now with respect to $\mathrm{A}$, we always get direction of $\overrightarrow{\mathrm{L}}$ 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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