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 bubb

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 : [2026]

Smart Achievers · Accepted Answer

(4)

$Using volume conservation$

$3 (\frac{4}{3} π r^{3}) = (\frac{4}{3} π R^{3})$

$R = 3^{1 / 3} r$

$\frac{V_{i}}{V_{f}} = \frac{\frac{k q}{r}}{\frac{k (3 q)}{R}} = \frac{R}{3 r} = \frac{3^{1 / 3} r}{3 r} = \frac{1}{3^{2 / 3}}$

Solution

Q.
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 : [2026]

1 $3^{2 / 3} : 1$

2 $1 : 3^{1 / 3}$

3 $1 : 2^{2 / 3}$

4 $1 : 3^{2 / 3}$

Ans.
(4)

$Using volume conservation$

$3 (\frac{4}{3} π r^{3}) = (\frac{4}{3} π R^{3})$

$R = 3^{1 / 3} r$

$\frac{V_{i}}{V_{f}} = \frac{\frac{k q}{r}}{\frac{k (3 q)}{R}} = \frac{R}{3 r} = \frac{3^{1 / 3} r}{3 r} = \frac{1}{3^{2 / 3}}$

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Solution

Q. 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 : [2026]

1 32/3:1

2 1:31/3

3 1:22/3

4 1:32/3

Ans. (4) Using volume conservation 3(43πr3)=(43πR3) R=31/3r ViVf=kqrk(3q)R=R3r=31/3r3r=132/3