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 point such that-

Options

A. h = R
B. `h = R/3`
C. `h =R/2`
D. `h = (2R)/3`

Answer

B

Explanation

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`