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. (a) `R[2+(1)/(2sqrt2)]`
B. (b) `R[1+(1)/(2sqrt2)]R`
C. (c) `3R`
D. (d) None of these

Answer

A

Explanation

Applying conservation of energy, we get
`2mgR-mgR/sqrt2=1/2m u^2impliesu=sqrt(4gR-sqrt2gR)`

`H_(max)=R+R/sqrt2+(u^2sin^2 45^@)/(2g)`
`=R+R/sqrt2+(4gR-sqrt2gR)/(2gxx2)`
`=2R+R/sqrt2-(R)/(2sqrt2)R[2+(1)/(2sqrt2)]`