Question 106 of 311

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

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Answer: 20

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$T\cos \theta =mg=10\times {10}^{-6}\times 10={10}^{-4}$
$T\sin \theta =\dfrac{9\times {10}^{9}\times {q}^{2}}{0.04}=F$
$\tan \theta ==\dfrac{0.1}{\sqrt{0.24}}=\dfrac{F}{mg}$
$q=\dfrac{2\sqrt{10}}{3\sqrt{\sqrt{24}}}\times {10}^{-8}$
$0.95\times {10}^{-8}=\dfrac{a}{21}\times {10}^{-8}$
$a=20$