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.
75D
32D
54D
D
A
75D
B
54D
C
D
D
32D
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Solution
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The correct option is C54D 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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