Q. 27 identical drops of mercury are charged simultaneously to the same potential of 10 V each. Assuming drops to be spherical, if all the charged drops are made to combine to form one large drop, then the potential of larger drop would be
A) 45 V
B) 135
C) 270 V
D) 90 V
Explanation
(d) Radius of big drop, $R = 3\ r$
$\left\lbrack \because\frac{4}{3}\pi R^{3} = 27 \times \frac{4}{3}\pi r^{3} \right\rbrack$
$V = \frac{27q}{4\pi\varepsilon_{0}R_{\ }} = \frac{27q}{4\pi\varepsilon_{0}({3r)}_{\ }}$
$= 9\left( \frac{q}{4\pi\varepsilon_{0}r_{\ }} \right) = 9 \times 10 = 90\ $V
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.