One has to throw a particle from one side of a fixed sphere, in a diameterical plane to another side such that it just grazes the sphere. Minimum possible speed for this is `sqrt(2gR(sqrt(alpha)+sqrt(beta)))`. Find `alpha+beta`

Explanation

`(2V^(2)sinthetacostheta)/(g)=2RsinthetarArrv^(2)=(Rg)/(costheta)`
`u^(2)=V^(2)+2gR(1+costheta)`
`u^(2)=(Rg)/(costheta)+2gR+2gR cos theta`
`u^(2)=Rg(1+2cos^(2)g)/(costheta)+2gR`
for `u` to be minimum `(1+2cos^(2)theta)/(costheta)="min"`
`rArr cos theta=(1)/(sqrt(2)) rArr theta=pi//4`
`u_("min")=sqrt(sqrt(2Rg)+2gR+sqrt(2)Rg)=sqrt(2gR(sqrt(2)+1))`