The system of simple pendulum is immersed in liquid of a density `rho_(l)`. Prove that its new period of oscillation inside the liquid will be `T = 2pi sqrt((l)/(g(1-(rho_(l))/(rho_(s)))))` where `rho_(s)` is density of bob.

Explanation

To prove that the new period of oscillation of a simple pendulum immersed in a liquid of density \( \rho_l \) is given by

\[ T = 2\pi \sqrt{\frac{l}{g \left(1 - \frac{\rho_l}{\rho_s}\right)}} \]

where \( \rho_s \) is the density of the bob, we will follow these steps:

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