Question

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is $r$. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become :

• A. $\left( \frac{2r}{3} \right)$
• B. $\left( \frac{1}{\sqrt{2}} \right)$
• C. $\left(\frac{r}{\sqrt[3]{2}}\right)$
• D. $\left( \frac{2r}{\sqrt{3}} \right)$

Answer 1

Answer: (C)

$\left(\frac{r}{\sqrt[3]{2}}\right)$

Answer 2

tan$\theta = \frac{F}{mg}$
$\Rightarrow \frac{r/2}{y} = \frac{kq^2}{r^2mg} \Rightarrow y \propto r_3$
Therefore $\left(\frac{r'}{r}\right)^3 = - \frac{y/2}{y} \Rightarrow r' \left(\frac{1}{2}\right)^{1/3}$