Consider a solid sphere of radius $R$ floating in a pond with half of the sphere submerged. The sphere is pushed vertically downwards at the topmost point and released, such that it executes a simple harmonic motion. Acceleration due to gravity is $g$. What is the time period of oscillation?

One mole of an ideal gas of volume $V$ and temperature $T$ is allowed to expand adiabatically to volume $2 V$ while doing no external work. The universal gas constant is $R$. What is the pressure of the gas after expansion?

Two identical boxes contain the same ideal gas. Let $\left(n_1, \lambda_1, T_1\right)$ and $\left(n_2, \lambda_2, T_2\right)$ be the number density, mean free path and temperature of the gas in the first and the second box, respectively. One of the boxes is empty into the other one. What will be the mean free path? $\lambda$ and temperature $T$ of the gas now?

Consider two point charges $+q$ and $+2 q$ fixed on the $x-y$ plane at $(-\ell / 2,0)$ and $(+\ell / 2,0)$ respectively. Another point charge $-q$ having mass $m$ is released from rest at $(0,(\sqrt{3} / 2) \ell)$ on the $x y$ plane, as shown in the figure The permittivity of free space is $\epsilon_0$. What is the acceleration of the charge $-q$ at the time of release?