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.

  • \( g = 10\text{ m/s}^2\).

This is a part of my set: Aniket's Mechanics Challenges.

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