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The angular momentum of a point mass about the origin is L = 2*alpha*t*ln(t/(t+1)) k-hat, where alpha is a positive constant and t is time in seconds. Which of the following statements are correct? (A) The torque on the mass as a function of time is 2*alpha * [1/(t+1) + ln(t/(t+1))] k-hat. (B) The mass can pass through the point (0, 0, 4). (C) If the particle is at (0, 2, 0) when t = 1 s, then the x-component of its momentum at t = 1 s is alpha*ln(2). (D) If the particle is at (0, 2, 0) when t = 1 s, then the z-component of its momentum at t = 1 s is zero.

1. (A), (B) and (C) only
2. (A), (C) and (D) only
3. (B), (C) and (D) only
4. (A), (B), (C) and (D)

Correct answer: (A), (C) and (D) only

Solution

Torque is obtained by differentiating L. The direction of L (always z-axis) combined with the given position constrains the momentum components.

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