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Question

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.
885725_430b6c18edc74341b03b956017e659f1.png
  1. 75D
  2. 32D
  3. 54D
  4. D

A
75D
B
54D
C
D
D
32D
Solution
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The correct option is C 54D
Let total energy is conserved,
Total mechanical energy at start = Total mechanical energy at 'B'
mgh = 12mv2B +mgD ...........(1)
Minimum speed required to complete rotation is, vb=rg=Dg/2
Hence equation (1) becomes,
mgh = 12mD2g + mgD
hence, h=5D4

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