Question

Two small spheres each of mass $10\text{mg}$ are suspended from a point by threads $0.5\text{m}$ long. They are equally charged and repel each other to a distance of $0.20\text{m}$. Then charge on each of the sphere is $\frac{a}{21}\times {10}^{-8}\text{C}$. The value of ${}^{\prime }{a}^{\prime }$ will be______. [Take $g=10{\text{m/s}}^2$]

Answer 1

From F.B.D
$T\sin \theta =\frac{k{q}^2}{d^2}$ and $T\cos \theta =mg$
Dividing them,
$mg\tan \theta =\frac{k{q}^2}{d^2}$
$q=\sqrt{\frac{mg\tan \theta }{25k}}$
$q=\sqrt{\frac{10\times {10}^{-6}\times 10\times 1}{\sqrt{24}\times \left(25\right)9\times {10}^9}}$
$q=\frac{2}{3}\sqrt{\frac{{10}^{-4}\times 4}{\sqrt{24}\times 25\times 4\times 9\times {10}^9}}$
$q=\frac{2}{3}\sqrt{\frac{{10}^{-4}}{\sqrt{24}\times {10}^{11}}}$
Thus $\frac{a}{21}\times {10}^{-8}=\frac{2}{3}\times \sqrt{\frac{{10}^{-15}}{\sqrt{24}}}=\frac{2}{3}\times \sqrt{\frac{{10}^{-16}}{0.49}}$
$a=\frac{2\times 21}{3\times 0.7}=20$