Question

Twenty seven identical drops of mercury are charged simultaneously to the same potential of 10 units. Assuming the drops are made to combine to form one large drop, then its potential is

• A. 45 units
• B. 135 units
• C. 270 units
• D. 90 units

Answer 1

Answer: (D)

90 units

Answer 2

Let r be the radius of small drop and R, the radius of big drop. Then

$\frac{4}{3}\pi R^{3} = (27)\frac{4}{3}\pi r^{3}$or $R = 3r$

Charge on bigger drop = 27q

$\text{V } = \ \frac{1}{4\pi\varepsilon_{0}}\text{ x }\frac{\text{27q}}{\text{3 }r} = 9\left\lbrack \frac{1}{4\pi\varepsilon_{0}}\text{ x }\frac{q}{r} \right\rbrack$= 9 x 10 = 90units