A particle of mass m slides on a frictionaless surface ABCD, starting from rest as shown in figure. The part BCD is a circular arc. If it looses contact at point P, the maximum height attained by the particle from point C is

Options

A. `R[2+(1)/(2sqrt(2))]`
B. `R[2-(1)/(2sqrt(2))]`
C. `3R`
D. none of these

Explanation

Apply conservation of energy
`2mgR-mg"(R )/(sqrt(2))=(1)/(2)mu^(2)`
`rArr u=sqrt(4gR-sqrt(2)gR)`
`H_(max)=R+(R )/(sqrt(2))+(u^(2)sin^(2)45^(@))/(2g)=R+(R )/(sqrt(2))+(4gR-sqrt(2)gR)/(2gxx2)`
`=2R+(R )/(sqrt(2))-(R )/(2sqrt(2))=R[2+(1)/(2sqrt(2))]`