A small block of mass m=1 kg is placed over a wedge of mass M=4 kg as shown in figure. Mass m is released from rest. All surfaces are smooth. Origin O is as shown. `(g=10 m//s^(2))`

Final velocity of the wedge is ...... `m//s`.

Options

A. `sqrt3`
B. `sqrt2`
C. `(1)/(sqrt2)`
D. `(1)/(sqrt3)`

Answer

B

Explanation

By appplying conservation of momentum
`mv_(1) + Mv_(2) = 0 rArr v_(1) = -4v_(2)` …..(i)
By applying conservation of energy
`(1)/(2)mv_(1)^(2) + (1)/(2)Mv_(2)^(2) = mgh rArr (v_(1)^(2))/(2) + 2v_(2)^(2) = 20` ……(ii)
`v_(2) = sqrt2m//s , v_(1) = 4 sqrt2 m//s`.