A mass M hangs on a massless rod of length l which rotates at a… | JEE Main 2021 (17 Mar, Shift 1)

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Angular Momentum & its Conservation

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

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Answer: (a)

About A (centre of the circle): $\vec r\perp\vec v$ in the horizontal plane, so $\vec L_A=Mrv\,\hat k$ — fixed magnitude and direction.
About B: $\vec r_B$ is along the rod, so $\vec L_B=M\vec r_B\times\vec v$ is perpendicular to the rod; it has a constant magnitude $Mlv$ but its direction rotates with the mass.
So the answer is (a) $L_A$ is constant in magnitude and direction.

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Angular Momentum & its Conservation question from JEE Main 2021 (17 Mar, Shift 1)

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