Mathematics · Mechanics
A smooth semicircular wire track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R4 is attached to the lowest point O of the wire track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The ring is held stationary at point P such that the spring makes a 60° angle with the vertical. The spring constant is k = mg / R. Determine the tangential acceleration of the ring immediately after it is released, and the normal reaction at that position.
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Tangential acceleration = (√5 / 8) g, Normal reaction = 3√5mg / 8
- 2Tangential acceleration = (5√3 / 8) g, Normal reaction = 3mg / 8✓
- 3Tangential acceleration = (3 / 8) g, Normal reaction = 5√3mg / 8
- 4Tangential acceleration = (√38) g, Normal reaction = 5mg / 8
Correct answer
Tangential acceleration = (5√3 / 8) g, Normal reaction = 3mg / 8
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