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Q.

Two identical conducting spheres R and S have negative charges $Q_{1} and Q_{2}$ respectively, but $Q_{1} \neq Q_{2}$ . The spheres are brought to touch each other and then kept in their original positions, now the force between them is :

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a

greater than that before the spheres touched

b

less than that before the spheres touched

c

same as that before the spheres touched

d

zero

answer is A.

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Detailed Solution

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Question Image

$F_{final} = \frac{{KQ}_{1} Q_{2}}{R^{2}}$

After contact charge on both sphere will be $- (\frac{Q_{1} + Q_{2}}{2})$

Final

Question Image

$F_{final} = \frac{K {\{\frac{Q_{1} + Q_{2}}{2}\}}^{2}}{R^{2}}$

As we know for two numbers

Arithmetic mean > Geometric mean

So, $\frac{Q_{1} + Q_{2}}{2} > \sqrt{Q_{1} Q_{2}}$

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