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

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 LA which lies in the positive z direction and the angular momentum of M about B is LB. The correct statement for this system is:

  1. LA and LB are both constant in magnitude and direction
  2. LB is constant in direction with varying magnitude
  3. LB is constant, both in magnitude and direction
  4. LA is constant, both in magnitude and direction

Solution

We know, L→=m(r→×v→)

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

Asked in: JEE Main 2021 (17 Mar Shift 1)

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