MHT CET202520 Apr 2025Morning ShiftPhysicsElectrostaticsActual
' n ' small spherical drops of same size which are charged to ' V ' volt each coalesce to form a single big drop. The potential of the big drop is
Options
- Av n
- Bn V
- Cn ^ 1 / 3 ~V
- Dn ^ 2 / 3 . V
Correct answer
D. n ^ 2 / 3 . V
Step-by-step solution
The potential of a small drop with charge q and radius r is V = 1 4 ₀ q r . When n such drops coalesce, both volume and charge are conserved. For volume, n 4 3 r^3 = 4 3 R^3 , yielding R = n^ 1/3 r . The total charge becomes Q = nq . The potential of the large drop is then V' = 1 4 ₀ Q R = 1 4 ₀ nq n^ 1/3 r . Simplifying gives V' = n^ 2/3 ( 1 4 ₀ q r ) = n^ 2/3 V . Final answer: V' = n^ 2/3 V