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?

The correct option is C (54D)
Let total energy is conserved,
Total mechanical energy at start = Total mechanical energy at 'B'
mgh =1/2mv²B +mgD.. (1)
Minimum speed required to complete rotation is, vb=√(gD/2)
Hence equation (1) becomes,
mgh =1/2m(Dg)+ mgD
hence,h=5D/4