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A block of mass m is placed on a smooth ...

A block of mass m is placed on a smooth sphere of radius R. It slides when pushed slightly. At what vertical distance h, from the top, will it leave the sphere?

A

`(R )/(4)`

B

`(R )/(3)`

C

`(R )/(2) `

D

`R`

Text Solution

Verified by Experts

The correct Answer is:
B

Let the block leave the sphere at point B, which is at a distance h from the top of the sphere.
`therefore (mv^2)/( R ) =mg cos theta -N`
where N is the normal reaction and v is the velocity of block at point B.
When the block leaves the sphere at point B, the normal reaction N becomes zero.
`therefore (mv^2)/( R ) = mg cos theta or cos theta =(v^2)/(Rg)`
From figure,` cos theta = (R-h)/( R)`
` therefore (R-h)/(R ) = (2 gh)/(Rg) " " [ :. v= sqrt(2 gh)]`
` or R-h =2h or 3h=R or h=(R )/(3 )`
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