Two small spheres each of mass $10 \mathrm{mg}$ are suspended from a point by threads $0.5 \mathrm{~m}$ long. They are equally charged and repel each other to a distance of $0.20 \mathrm{~m}$. The charge on each of
the sphere is $\frac{\mathrm{a}}{21} \times 10^{-8} \mathrm{C}$. The value of 'a' will is_________.
[Given $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ]
$\mathrm{T} \cos \theta=\mathrm{mg}=10 \times 10^{-6} \times 10=10^{-4}$
$\mathrm{T} \sin \theta=\frac{9 \times 10^{9} \times \mathrm{q}^{2}}{0.04}=\mathrm{F}$
$\tan \theta==\frac{0.1}{\sqrt{0.24}}=\frac{F}{m g}$
$\mathrm{q}=\frac{2 \sqrt{10}}{3 \sqrt{\sqrt{24}}} \times 10^{-8}$
$0.95 \times 10^{-8}=\frac{\mathrm{a}}{21} \times 10^{-8}$
$a=20$
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