A ball of mass `m` is released from A inside a smooth wedge of mass `m` as shown in figure. What is the speed of the wedge when the ball reaches point B?

Options

A. `((gR)/(3sqrt2))`
B. `sqrt(2gR)`
C. `((5gR)/(2sqrt3))^(1//2)`
D. `sqrt(3)/(2)gR`

Answer

A

Explanation

`COLM rArr m(v_(1) cos 45^(@) + v_(2)) + mv_(2) = 0`
`rArr v_(1) = 2sqrt2.v_(2)`
`COME rArr K_(1) + U_(1) = K_(f) + U_(f)`
`rArr 0 + (mgR)/(sqrt2) = (1)/(2) mv_(2)^(2)`
`(1)/(2)m[(v_(1)^(2))/(2) + ((v_(1))/(sqrt2) - (v_(1))/(2sqrt2))^(2)] rArr sqrt((gR)/(3sqrt2))`