Question

Two identical pith balls are charged by rubbing against each other. they are suspended from a horizontal rod through two strings of length 20 cm each, the separation between the suspension points being 5 cm. In equilibrium, the sepaation between the balls is 3 cm. Find the mass of each ball and the tension in the stirngs. The charge on each ball ahs a magnitude $2.0\times {10}^{-8}$ C.

Answer 1

$T\cos \theta =mgT\sin \theta =F$

$\sin \theta =\frac{1}{20}$
$\cos \theta =\sqrt{1-{\left(\frac{1}{20}\right)}^2}$
From equation (i) and (ii)
$\tan \theta =\frac{F}{mg}\therefore m=\frac{F}{g\tan \theta }orm=\frac{9\times {10}^9\times (2\times {10}^{-8}{)}^2}{9\times {10}^{-4}\times .98\times \tan \theta }=8.2gT=\frac{F}{\sin \theta }=\frac{9\times {10}^9\times (2\times {10}^{-8}{)}^2}{9\times {10}^{-4}\times \frac{1}{20}}T=8.2\times {10}^{2}N$