A hollow sphere of mass m and radius R is placed on smooth gound. A particle of mass m is projected with velocity `v_(0)` and angle `theta` lowest point a inside the sphere as shown in diagram if particle strikes the sphere at a point which is on horizontal level of centre and at that moment particle is at highest point. The collision between particle and sphere is elastic. The value of `v_(0)` is

Options

A. `v_(0)=sqrt((Rg)/(costheta))`
B. `v_(0)=(sqrt(2Rg))/(sintheta)`
C. `(2sqrt(Rg))/(tantheta)`
D. `v_(0)=(sqrt(Rg))/(2)[1+cos^(2)theta]`

Answer

B

Explanation

Conservation of energy
`(1)/(2)mv_(0)^(2)=mgR+(1)/(2)mv^(2),v=v_(0)costheta`
`(1)/(2)v_(0)^(2)=gR+(v_(0)^(2)cos^(2)theta)/(2)`
`v_(0)^(2)[1-cos^(2)theta0]=gR`
`v_(0)=(sqrt(2gR))/(sintheta)`