27 identical drops are charged at 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be V.

Question

27 identical drops are charged at 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be V. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

q arrow nq n (4/3) π r 3=(4/3) π( r prime)3 ⇒ r prime= n (1/3) r V =( kq / r ) propto ( n / n 1 / 3) propto n 2 / 3 propto 272 / 3 ⇒ v prime=9 V =9 × 22=198

Q. $27$ identical drops are charged at $22 V$ each. They combine to form a bigger drop. The potential of the bigger drop will be ___ $V$ .

$q \to n q$
$n \frac{4}{3} π r^{3} = \frac{4}{3} π (r^{'})^{3}$
$\Rightarrow r^{'} = n^{\frac{1}{3} r}$
$V = \frac{k q}{r} \propto \frac{n}{n ^{1/3}} \propto n^{2/3} \propto 2 7^{2/3}$
$\Rightarrow v^{'} = 9 V = 9 \times 22 = 198$

Q. 27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be ___V.

q→nq n34​πr3=34​π(r′)3 ⇒r′=n31​r V=rkq​∝n1/3n​∝n2/3∝272/3 ⇒v′=9V=9×22=198

Q. $27$ identical drops are charged at $22 V$ each. They combine to form a bigger drop. The potential of the bigger drop will be ___ $V$ .

$q \to n q$
$n \frac{4}{3} π r^{3} = \frac{4}{3} π (r^{'})^{3}$
$\Rightarrow r^{'} = n^{\frac{1}{3} r}$
$V = \frac{k q}{r} \propto \frac{n}{n ^{1/3}} \propto n^{2/3} \propto 2 7^{2/3}$
$\Rightarrow v^{'} = 9 V = 9 \times 22 = 198$