A smooth hoop lie as on a smooth horizontal table and is fixed. A particle is projected on the table form a point A on the inner circumference of the hoop at angle `theta` with radius vector . If e be the coefficient of restitution and the particle returns to the point of projection after two successive impacts. The final angle `theta'` made by velocity vector with radius of hoop is

Options

A. `tan theta' = ( e^(2))/( ( 1+ e^(2))) tan theta `
B. `tan theta' = e^(2) tan theta `
C. `tan theta ' = ( tan theta )/( e^(2))`
D. `tan theta' = ( tan theta)/( e )`

Answer

C