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A particle slides on the surface of a fi...

A particle slides on the surface of a fixed smooth sphere starting from the topmost pont. Find the angle rotated by the radius through the particle, when it leaves contact with the sphere.

Text Solution

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The correct Answer is:
A, B, C
Let the velocity be v when the body leaves the surface.
From the free body diagram
`(mv^2)/R=mgcostheta` [because normal reaction]………i
`v^2=Rgcostheta` ……i

Again, from work energy
`principle change in K.E. =work done
`rarr 1/2 mv^2-0=mg(R-Rcostheta)`
`rarr v^2=2gR(1-costheta)` ........ii
From i and ii
`Rgcostheta=2gR(1-costheta)`

`3gRcostheta-2gR`
`costheta=2/3`
`theta=cos^-1(2/3)`
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