A particle is projected with velocity `u` horizontally from the top of a smooth sphere of radius a so that it slides down the outside of the spher. If the particle leaves the outsides down th eoutside of the sphere. If the particle leaves the sphere when it has fallen a height `(a)/(4)` , the value of `u` is

Options

A. `sqrt(ag)`
B. `(sqrt(ag))/(4)`
C. `(sqrt(ag))/(2)`
D. `(sqrt(ag))/(3)`

Answer

C

Explanation

At the time of leaving contact at `P`

`N=0`
:. `mgcostheta=(mv^(2))/(a)=(m(u^(2)+2gh))/(a)`
:. `g(3a//4)=(u^(2)+2g(a//4))/(a)`
`u=(sqrt(ag))/(2)`