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Question

A body initially at rest and sliding along a frictionless track from a height h just completes a vertical circle of diameter AB=D. What is the height h equal to?


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Solution

Step1: Given data

A body initially at rest and sliding along a frictionless track from a height h

A vertical circle of diameter AB=D.

Step2: Formula used

Potential energy, P.E.=mgh

Kinetic energy, K.E.=12mv2

Step3: Calculating the height

The energy at the top= The energy at the bottom
At the top, there is only potential energy and at the bottom, the energy is completely kinetic, so,

mgh=12mv2h=v22g

For completing the vertical circle, the velocity at the lowest point must satisfy the condition,

v5gr where r is the radius and equal to half of the diameter.

Now, the value of h becomes,

h=5gr2gh=54D

Hence, the height h is equal to 54D.


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