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A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB=D. The height h is equal to

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a
32D
b
D
c
75D
d
54D

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detailed solution

Correct option is D

As body is at rest initially, i.e., speed=0At point A, speed=v As track is frictionless, so total mechanical energy will remain constant.∴  (T.M.E)i=(T.M.E)f0+mgh=12mv2+0 or   h=v22g For completing the vertical circle, v≥5gR∴  h=5gR2g=52R=54D

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