# SHM of liquid

A V-shaped tube attached to the ground with its vertex. It's one leg makes an angle of $$30 ^\circ$$, and the other leg makes an angle of $$60 ^\circ$$ with the horizontal. The tube is filled with a liquid in a total length of $$1\text{ m}$$. Now the liquid at one side is displaced a little.Find the Time - period of SHM.

Your answer can be represented as $\sqrt{\dfrac{a \pi^b}{c (\sqrt{d} + 1)}} \; ,$

where $$a,b,c$$ and $$d$$ are positive integers with $$a,c$$ coprime and $$d$$ square-freee.

Enter your answer as $$a + b + c + d$$.

Details and Assumptions:

• Neglect surface tension , viscuous force and friction.

• $$g = 10\text{ m/s}^2$$.

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