Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be

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3 F/2

3F / 4

2 F

answer is B.

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Detailed Solution

Let $q_{A} = q_{B} = q$
Question Image
When C is placed in contact with A, charge on A & C will be $= \frac{q}{2}$
& C will be $= \frac{q}{2}$
Now C is placed in contact with B, charge on B & C will be $= \frac{q + \frac{q}{2}}{2} = \frac{3 q}{4}$
Now,

$Force between A and C F_{1} = k (\frac{3 q}{4} \frac{q}{2}) {(\frac{2}{r})}^{2} = k \frac{3 q^{2}}{2 r^{2}} = \frac{3}{2} F$

$Force between B and C k (\frac{3 q}{4} \frac{3 q}{4}) \frac{4}{r^{2}} = k \frac{9 q^{2}}{4 r^{2}} = \frac{9 F}{4}$

$Net force = \frac{3 F}{4}$

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