Question

Two small balls having equal positive charges $Q$ $\text{(coulomb)}$ on each are suspended by two insulating strings of equal length $L$ $\text{(metre)}$ from a hook fixed to a stand. The whole setup is taken in a satellite into space where there is no gravity $($state of weightlessness$)$. The angle between the two strings and the tension in each string is

• A. ${180}^{\circ },\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{4L^2}\text{N}$
• B. ${75}^{\circ },\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{L^2}\text{N}$
• C. ${120}^{\circ },\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{3L^2}\text{N}$
• D. ${60}^{\circ },\frac{1}{4\pi {ϵ}_0}\frac{3Q^2}{2L}\text{N}$

Answer 1

The correct option is A ${180}^{\circ },\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{4L^2}\text{N}$

Free body diagram:


There is a condition of weightlessness in a satellite. Therefore, $mg=0$.

Due to electrostatic force of repulsion between the balls, the string would become horizontal. Therefore, angle between the two small balls $={180}^{\circ }$.

From free body diagram, the tension in the string will be equal to the electrostatic force of repulsion,

$\Rightarrow T=F_e$

$\Rightarrow T=\frac{1}{4\pi {ϵ}_0}\frac{Q\times Q}{(2L{)}^2}$

$\Rightarrow T=\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{4L^2}\text{N}$

Hence, option (a) is correct answer.