Material point and curve wedge

1. The problem statement, all variables and given/known data

I think that the image is clear.
There isn’t friction, not the material point with wedge, not the wedge with the floor.

At time t=0 the material point start to move, I need to find the final speed of the two objects at time $t\rightarrow\infty$.

2. Relevant equations

I have used conservation of energy and momentum.

3. The attempt at a solution

So I have two equation:
$\frac{1}{2}m{v_m}^2+\frac{1}{2}M{v_M}^2 = mgR$

$m{v_m}+M{v_M}=0$

And the solution is ${v_m}=\sqrt{\frac{mgR}{\frac{1}{2}m+\frac{1}{2}\frac{m^2}{M}}}$

Am I wrong?

Attached Images
 Problem_1-7-2014.png (4.7 KB)

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