Figure shows a frictionless track at which a slider starts from rest at point A. Find the minimum value for the radius of curvature of track at point B, such that the slider remains in contact with the track.
A
20m
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B
10m
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C
40m
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D
25m
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Solution
The correct option is A20m From the law of conservation of mechanical energy between points A and B, Loss in potential energy = Gain in kinetic energy ⇒mgh=12mv2 ⇒v2=2gh .............(1) Here h is the height difference between point A and B.
At point B, mg−N=mv2r In critical case, N=0, v2=rg ⇒2gh=rg[ from (1)] ⇒r=2h ⇒r=2×10=20m[ from diagram ]