Rigid uniform Rod 'AB' of mass 'M' and Length 'L' is pulled slightly ( Gently ) at the bottom at time t=0 . when it just reaches the horizontal ground. Then Velocities of End's Point's .

\(\displaystyle{ V }_{ A }=\sqrt { \cfrac { a }{ b } (gL) } \\ \\ { V }_{ B }=\sqrt { \cfrac { c }{ d } (gL) } \).

Then Find The Value of \(a+b+c+d\)

**details and Assumptions**

\(\bullet\) All Surfaces are Perfectly Smooth.

\(\bullet\) Rod May not Necessarily remain always in contact with Vertical wall.

\(\bullet\) \(a,b,c,d\) all are positive integers , \(gcd(a,b)=1\) , \(gcd(c,d)=1\)

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