Question

Two small identical balls P and Q, each of mass $\frac{\sqrt{3}}{10}$ gram, carry identical charges and are suspended by threads of equal lengths. At equilibrium, they position themselves as shown in fig. What is the charge on each ball? Given $\frac{1}{4\pi {ϵ}_0}=9\times {10}^{9}N{m}^2{C}^{-2}$ and take $g=10m{s}^{-2}$

• A. ${10}^{-3}C$
• B. ${10}^{-5}C$
• C. ${10}^{-7}C$
• D. ${10}^{-9}C$

Answer 1

The correct option is C ${10}^{-7}C$


$Tcos{60}^{\circ }=F_E=9\times {10}^9\times \frac{q^2}{(0.3{)}^2}\Rightarrow \frac{T}{2}=q^2\times {10}^{+11}$ and
$Tcos{30}^{\circ }=mg$
$T\times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{10}\times {10}^{-3}\times 10$
$\Rightarrow T=2\times {10}^{-3}N$
$\Rightarrow q^2\times {10}^{11}=\frac{2\times {10}^{-3}}{2}$
$q={10}^{-7}C$