JEE Main 2025 — Electrostatics Question with Solution

A small bob of mass 100 mg and charge $+10\mu \mathrm{C}$ is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density ' $\sigma$ ' as shown in figure. If string subtends an angle of $45^{\circ }$ with the sheet at equilibrium the charge density of sheet will be :
(Given, ${\epsilon }_0=8.85\times 10^{-12}\frac{\mathrm{F}}{\mathrm{m}}$ and acceleration due to gravity, $g=10\mathrm{m}/{\mathrm{s}}^2$)