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A metal sphere $A$ of radius a carrying charge $- Q$ and another metal sphere $B$ of radius $2 a$ carrying charge $2 Q$ are placed at a large distance $d (d ≫ a)$ from each other. The Coulomb force between them has magnitude $F$ . The spheres are brought in contact with each other and are kept at a distance $d / 3$ . The force of repulsion between them now is:

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$\frac{1}{4} F$

$\frac{2}{3} F$

$F$

$\frac{3}{8} F$

answer is C.

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Detailed Solution

Initially $F = \frac{K 2 Q^{2}}{d^{2}}$ . After $A$ and $B$ are bought in contact, the total charge

$- Q + 2 Q = Q$ distributes on, A and B in proportion to their radii ,

that is, $\frac{Q}{3} and \frac{2 Q}{3}$ respectively .

Now $F^{'} = \frac{K \frac{2 Q^{2}}{9}}{\frac{d^{2}}{9}} = \frac{K 2 Q^{2}}{d^{2}} = F$ .

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