Question

Two similar balls of mass ‘m’ are hung by a silk thread of length L and carry similar charges Q as in figure Assuming the separation to be small, the separation between the balls (denoted by x) is equal to

• A. ${\left[\frac{Q^2.2L}{4\pi {ϵ}_0.mg}\right]}^{\frac{1}{3}}$
• B. QLlmg
• C. $\frac{QL}{mg}$
• D. $\frac{Q^{2}L}{2\pi mg}$

Answer 1

The correct option is A ${\left[\frac{Q^2.2L}{4\pi {ϵ}_0.mg}\right]}^{\frac{1}{3}}$

$Tan\theta =\frac{F}{mg}$
$\theta =\frac{F}{mg}$
$F=\theta mg$
$\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{x^2}=\frac{x}{2L}\times mg$
$x^3=\frac{Q^2}{4\pi {ϵ}_0}\frac{2L}{mg}$
$x={\left[\frac{Q^2}{4\pi {ϵ}_0}\frac{2L}{mg}\right]}^{\frac{1}{3}}$