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A body initially at rest slides 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

Asked in NEET 2018 · Energy in vertical circular motion

Figure: Energy in vertical circular motion
Answer: (4) 5/4D

Step-by-step solution

Given: the body starts from rest at height h and just completes a vertical loop of diameter D, so radius R=D/2.

Idea: a loop is only just completed when the speed at the bottom is √5gR — the least speed that still leaves √gR at the top.

Speed at the bottom of the loop, from the slide: v=√2gh.

Condition: √2gh=√5gR=√(5gD)/2.

2gh=(5gD)/2.

h=(5D)/4.

Why the other options are wrong

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