Question 44

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

Three bubbles coalesce: volume conserved: $$3 \times \frac{4}{3}\pi r^3 = \frac{4}{3}\pi R^3$$, so $$R = 3^{1/3}r$$. Charge: $$3q$$ total.

$$V_r/V_R = \frac{kq/r}{k(3q)/R} = \frac{R}{3r} = \frac{3^{1/3}}{3} = 3^{-2/3}$$. Ratio = $$1:3^{2/3}$$.

The answer is Option 2.

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