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 big drop
`therefore((4)/(3)pir^(3))xx8=(4)/(3)piR^(3)`
`implies2r=R` . . . (i)
According to charge conservation
`8q=Q` . . . (ii)
Potential of one small drop
`(V')=(q)/(4piepsi_(0)r)`
similarly, potential of big drop
`(V)=(Q)/(4piepsi_(0)R)` ltBrgt Now, `(V')/(V)=(q)/(Q)xx(R)/(r)`
`implies(V')/(20)=(q)/(8q)xx(2r)/(r)`
[from eqs. (i) and (ii)]
`thereforeV'=5`volts