JEE PYQ: Capacitance Question 11
Question 11 - 2021 (26 Feb Shift 2)
27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ____ times that of a smaller drop.
Show Answer
Answer: 243
Solution
For self energy of sphere (conducting) $U = \frac{kq^2}{2r}$. For small drop $U_s = \frac{kq^2}{2r}$. After combine: volume remains same, so $\frac{4}{3}\pi r^3 \times n = \frac{4}{3}\pi R^3$. $R = (n)^{1/3}r = 3r$. For large drop $U_f = \frac{k(nq)^2}{2 \times 3r}$. $\frac{U_f}{U_s} = (n)^{5/3} = (27)^{5/3} = 243$.
BETA
