Question

$1000$ small water drops each of radius ${}^{\prime }{r}^{\prime }$ and charge ${}^{\prime }{q}^{\prime }$ coalesce together to one spherical drop. The potential of the big drop is larger than that of the smaller drops by a factor of:

• A. $1000$
• B. $100$
• C. $10$
• D. $1$

Answer 1

The correct option is B $100$

$V_{small}=k\frac{q}{r}$

If the radius of big drop is $R$ , $\frac{4}{3}\pi R^3=1000\frac{4}{3}\pi r^3\Rightarrow R=10r$.

and charge of big drop , $Q=1000q$

Now $V_{big}=k\frac{Q}{R}=k\frac{1000q}{10r}=100k\frac{q}{r}=100V_{small}$