Physics Question from JEE Main 2025 · 2 April, Shift 1

A small bob of mass $100 \, \text{mg}$ and charge $+10 \, \mu\text{C}$ is connected to an insulating string of length $1 \, \text{m}$. It is brought near to an infinitely long non-conducting sheet of charge density $\sigma$. If the string subtends an angle of $45^\circ$ with the sheet at equilibrium, the charge density of the sheet will be:

(Given, $\epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m}$ and acceleration due to gravity, $g = 10 \, \text{m/s}^2$)