The centres of two identical small conducting spheres are 1 m apart. They carry charges of opposite kind and attract each other with a force F. When they are connected by a conducting thin wire they repel each other with a force $\frac{F}{3}$ . What is the ratio of magnitude of charges carried by the spheres initially?

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2: 1

4: 1

3: 1

1 : 1

answer is C.

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Detailed Solution

From Coulomb's law,

$q_{1} q_{2} \propto F$ $[∵ r = 1 m] \dots (i)$

As the charges are of opposite nature, when they are connected by a wire the charge on each sphere will become $\frac{q_{1} - q_{2}}{2}$

$(\frac{q_{1} - q_{2}}{2}) (\frac{q_{1} - q_{2}}{2}) \propto \frac{F}{3}$

Dividing Eq. (i) by Eq. (ii), And solving for $\frac{q_{1}}{q_{2}}$ we get

$\frac{q_{1}}{q_{2}} = \frac{3}{1}$

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