A Rigid Problem About A Rigid Hoop

Classical Mechanics Level 3

A rigid hoop can rotate about the center. Two massless strings are attached to the hoop, one at \( A \), the other at \( B \). These strings are tied together at the center of the hoop at \( O \), and a weight \( G \) is suspended from that point. The strings have a fixed length, regardless of the tension, and the weight \( G \) is only supported by the strings. Originally \( OA \) is horizontal.

Now, the outer hoop will start to slowly rotate \( 90^\circ \) clockwise until \( OA \) will become vertical, while keeping the angle between the strings constant and keeping the object static. Which of the following statements about the tensions \( T_1 \) and \( T_2 \) in the two strings is correct?

Note: This problem appeared on the 2012 F = ma exam.

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Ahaan Rungta by Ahaan Rungta
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