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 :
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Question

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 :

G1 Physics · Accepted Answer

Let the radius and charge of each small bubble be r and q. After three identical bubbles coalesce, volume is conserved: 3(4πr³/3) = 4πR³/3. Therefore, R³ = 3r³, so R = ∛3 r. The total charge on the bigger bubble is Q = 3q. Potential of one initial bubble: V(initial) = kq/r. Potential of the final bubble: V(final) = k(3q)/R. Therefore, V(initial)/V(final) = (kq/r)/[3kq/R] = R/(3r) = ∛3/3 = 1/∛9. Hence, V(initial) : V(final) = 1 : ∛9. Correct option: D.