# Sliding Rod!

Rigid uniform Rod is pulled slightly ( Gently ) at the bottom at time $$t=0$$ . Then Find the angle $$\theta$$ from Horizontal as shown at which Rod will Loose it's contact with Vertical Smooth wall . If your answer can be expressed as : $$\tan { \theta } \quad =\quad \cfrac { a\sqrt { b } }{ c }$$. Then Find $$a+b+c$$

Details and assumptions

$$\bullet$$ All surfaces are perfectly smooth.

$$\bullet$$ $$gcd(a,c)=1$$

$$\bullet$$ $$b$$ is square free integer and $$a , b , c$$ all are integers.

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