`n` small drops of same size are charged to `V` volts each .If they coalesce to from a single large drop, then its potential will be -

Explanation

Let r be the radius of each small drop and R be the radius of bigger drop.
As volume of bigger drop = volume of n small drops
`:. (4)/(3) pi R^(3) = n xx (4)/(3) pi r^(3)`
As capacity varies directly as the radius,
`:.` Capacity of bigger drop becomes `n^(1//3)` times the capacity of each small drop.
Also, potential of bigger drop `= ("total charge")/("capacity")`
`:. V = (nq)/(4 pi in_(0) R) = (nq)/(4pi in_(0) n^(1//3) r) = n^(2//3) (q)/(4pi in_(0) r)`
`= n^(2//3)` times the potential of each small drops.