Correct Answer - A
Let the velocity of wedge be v.
Loss in PE=Gain in KE
`mgR cos 45^@=1/2mv^2+1/2m(v_1cos45^@-v)^2+1/2m(v_1sin45^@)^2`
From conservation of linear momentum
`m(v_1cos45^@-v)=mv`
Here `v_1` is the velocity of ball w.r.t. wedge, Solve to get
`v=((gR)/(3sqrt2))^(1//2)`