Physics - Elecrostatics Question with Solution | TestHub

$$\begin{array}{rl}& qE=mg\\ & 6\pi \eta rv=mg\\ & \frac{4}{3}\pi r^3\rho g=mg\\ & \therefore r={\left(\frac{3mg}{4\pi \rho g}\right)}^{1/3}\end{array}$$ Substituting the value of $r$ in Eq. (ii) we get, $$6\pi \eta v{\left(\frac{3mg}{4\pi \rho g}\right)}^{1/3}=mg$$ or $(6\pi \eta v{)}^3\left(\frac{3mg}{4\pi \rho g}\right)=(mg{)}^3$ Again substituting $mg=qE$ we get, $$(qE{)}^2=\left(\frac{3}{4\pi \rho g}\right)(6\pi \eta v{)}^3$$ or $qE={\left(\frac{3}{4\pi \rho g}\right)}^{1/2}(6\pi \eta v{)}^{3/2}$ $$\therefore q=\frac{1}{E}{\left(\frac{3}{4\pi \rho g}\right)}^{1/2}(6\pi \eta v{)}^{3/2}$$ Substituting the values we get , $$\begin{array}{rl}q=& \frac{7}{81\pi \times 10^5}\sqrt{\frac{3}{4\pi \times 900\times 9.8}\times 216{\pi }^3}\\ & \times \sqrt{{\left(1.8\times 10^{-5}\times 2\times 10^{-3}\right)}^3}\\ & =8.0\times 10^{-19}\mathrm{C}\end{array}$$ $\therefore$ correct option is $(\mathrm{d})$.