$m = 1$ kg and length $l=1$ m is placed along the hypotenuse side of a wedge lying on a friction less floor having mass $M =5$ kg and angle $60°$. At $t= 0$ the system is released from rest. Both the objects are free to move. Find the speed of the wedge when the rod makes an angle $30°$ with the floor.

A thin rod of massThe answer can be expressed as $\sqrt { \frac { a(\sqrt { 3 } -1) }{ b } }$. Find $a+b$.

**Notes**

- Take $g=10m/{ s }^{ 2 }$