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Question

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
20 m
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B
10 m
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C
40 m
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D
25 m
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Solution

The correct option is A 20 m
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,
mgN=mv2r
In critical case, N=0,
v2=rg
2gh=rg [ from (1) ]
r=2h
r=2×10=20 m [ from diagram ]

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