SHM in liquid

Classical Mechanics Level 4

A thin rod of length \(L\) and area of cross section \(S\) is pivoted at its lowest point P inside a stationary , homogeneous , non viscous liquid as shown in the figure.

The rod is free to rotate in a vertical plane about a horizontal axis passing through \(p\). The density of the material of the rod \(D_1\) is smaller than the density of liquid \(D_2\). The rod is displaced by a small angle \(θ\) from its equilibrium position and then released.

If the body performs Simple harmonic motion, calculate t's angular fequency \(\omega\)

Details and Assumptions

\(D_1 = 200 \text {units}\)

\(D_2 = 400 \text {units}\)

\(L = 20 \text {cm}\)

\(g =10 \dfrac {m}{s^2}\)

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