The potential of a large liquid drop when eight liquid drops are combined is 20 V. Then, the potential of each single drop was

Options

A. 10 V
B. `7.5 V`
C. 5 V
D. `2.5 V`

Answer

C

Explanation

Volume of 8 drops = Volume of bigger drop or
`((4)/(3) pi r^(3))xx 8 = (4)/(3)piR^(3)` or 2r = R ...(i)
Charge is conserved . `therefore 8q = Q`
`therefore V' = (q)/("capacity") = (q)/(4pieta_(0)r)` `V = (Q)/("capacity") = (Q)/(4pieta_(0)R)`
`therefore V'/V= (q)/(Q) xx(R)/(r)` or `V'/20 = (q)/(8q) xx (2r)/(r) = 1/4` or `V' = 5` volt.