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A particle originally at rest at the hig...

A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance `h` below the highest points, such that `h` is equal to

A

h = R

B

`h = R/3`

C

`h =R/2`

D

`h = (2R)/3`

Text Solution

Verified by Experts

The correct Answer is:
B
Suppose the particle leaves the circle at distance h below the highest point.
The point where it leaves the circle reaction is zero.
`mg cos theta = (mv^(2))/R rArr cos theta = v^(2)/(Rg)`……….(i)

Applying conservation of energy
`mgh =1/2 mv^(2) rArr v^(2) = 2gh`..... (ii)
From (i) and (ii)
`therefore cos theta = (2h)/R`
By geometry `to cos theta = (R-h)/R`
`therefore (2h)/R = (R-h)/R rArr h = R/3`
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