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Q.

Two identical balls each have a mass of 10 g. What charges should these balls be given so that their interaction equalizes the force of universal gravitation acting between them? The radii of the balls may be ignored in comparison to distance between them.

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a

$8.57 x 10^{- 11} C$

b

$6.34 x 10^{- 13} C$

c

$6.34 x 10^{- 11} C$

d

$8.57 x 10^{- 13} C$

answer is D.

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Detailed Solution

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If q charge is given to each ball, then

$\begin{array}{l} \frac{1}{4 {πε}_{o}} . \frac{q \times q}{r^{2}} = G \frac{m \times m}{r^{2}} or \\ q = \sqrt{4 {πε}_{o} G} \times m \\ Setting G = 6 .6 \times 10^{- 11} {Nm}^{2} {kg}^{- 2} and \\ m = 10 g = 10 \times 10^{- 3} kg, we get \\ q = 8 .57 \times 10^{- 13} C \end{array}$

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