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 . The angular momentum of M about points A is which lies in the positive z direction and the angular momentum of M about point . The correct statement for this system is : Option: 1 and are both constant in magnitude and direction   Option: 2 is constant, both in magnitude and direction Option: 3 is constant in direction with varying magnitude   Option: 4 is constant, both magnitude and direction

We know, $\overrightarrow{\mathrm{L}}=\mathrm{m}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{v}})$
Now with respect to 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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