Question

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

• A. 10 V
• B. 7.5V
• C. 5V
• D. 2.5V

Answer 1

Answer: (A)

Volume of 8 drops = Volume of big drop
$ \therefore $ $ \left( \frac{4}{3}\pi {{r}^{3}} \right)\times 8=\frac{4}{3}\pi {{R}^{3}} $
$ \Rightarrow $ $ 2r=R $ ...(i)
According to charge conservation
$ 8q=Q $ ...(ii)
We have $ V\propto \frac{1}{r} $
Or $ \frac{{{V}_{1}}}{{{V}_{2}}}=\frac{{{r}_{2}}}{n} $
$ \Rightarrow $ $ \frac{20}{{{V}_{2}}}=\frac{2r}{r} $
$ \Rightarrow $ $ {{V}_{2}}=10\,V $