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Question

A frictionless track ends in a circular loop of radius R. A body slides down the track from point A which is at height h = 5 cm. Maximum value of R, for a body to complete the loop successfully is

A
2 cm
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B
103 cm
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C
154 cm
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D
183 cm
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Solution

The correct option is A 2 cm
To just complete the circle, at the highest point, tension is zero and the gravitational force provides the necessary centripetal force.

Hence, mv2topR=mg.(i)

Applying conservation of energy at the top and bottom points,
12mv2bottom=mg×2R+12mv2top.(ii)
Substituting mv2top from (i) in (ii) and solving,
vbottom=5gR

But from given velocity at bottom=2gh

So, 2gh=5gR
2h=5RR=2 cm

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