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Question

A body is allowed to slide on a frictionless track from rest position under gravity. The track ends into a circular loop of diameter D. What should be the minimum height of the body in terms of D so that it may complete the loop successfully?

A
45D
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B
54D
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C
1D
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D
2D
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Solution

The correct option is B 54D
For the body to reach point B, the body must have least velocity of 5gR [From vertical circular motion] at A.
So, for a body falling from height h
Velocity [V]=2gH
2gh=5gr
[As r=D2]
2gh=5gD2
h=5D4

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