27 similar drops of mercury are maintained at 10V 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.
Answer (integer)
243
Solution
$(27)\left( {{4 \over 3}\pi {r^3}} \right) = {4 \over 3}\pi {R^3}$<br><br>R = 3r<br><br>Potential energy of smaller drop :<br><br>${U_1} = {3 \over 5}{{k{q^2}} \over r}$<br><br>Potential energy of bigger drop :<br><br>$U = {3 \over 5}{{k{Q^2}} \over R}$<br><br>$U = {3 \over 5}{{k{{(27q)}^2}} \over R}$<br><br>$U = {3 \over 5}k{{(27)(27){q^2}} \over {3r}}$<br><br>$U = {{(27)(27)} \over 3}\left( {{3 \over 5}{{k{q^2}} \over r}} \right)$<br><br>$U = 243\,{U_1}$
About this question
Subject: Physics · Chapter: Electrostatics · Topic: Electric Potential and Capacitance
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