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.

Step-by-step solution

27 4 3 π r 3 = 4 3 π R 3 R = 3 r Potential energy of smaller drop U 1 = 3 5 k q 2 r Potential energy of bigger drop : U = 3 5 k Q 2 R U = 3 5 k 27 q 2 R U = 3 5 k 27 27 q 2 3 r U = 27 27 3 3 5 k q 2 r U = 243 U 1