F=ma 2025 Problem 24

Physics · mechanics

Problem

Question: As shown in the figure, a massive bead is attached to the end of a massless rigid rod of length

L

. The other end of the rod is attached to an ideal pivot, which allows it to rotate frictionlessly in any direction. The rod is initially at angle

\theta

to the horizontal, and there is no gravitational force. Next, the bead receives an impulse directly into the page, giving it a speed

v

. How long does it take for the bead to return to its original position? (A)

2\pi L / v

. (B)

(2 \pi L / v) \sin \theta

. (C)

(2 \pi L / v) \cos \theta

. (D)

(2 \pi L / v) \cos^2 \theta

. (E)

(2 \pi L / v) \cos^2 (2\theta)

. *Note: This problem references figure(s): `image_question/F=MA_2025_24_1.png`*