Question

$27$ identical drops of mercury are charged simultaneously with the same potential of $10V$. Assuming the drop to the spherical, if all the charged drops are made to combine to form one large drop, then its potential will be _____ $V$.

• A. $40$
• B. $90$
• C. $160$
• D. $10$

Answer 1

The correct option is B $90$

The volume of spheres.
$27\times \frac{4}{3}\pi r^3=\frac{4}{3}\pi R^3$
where, $r$ and $R$ are the volume of smaller and bigger sphere respectively.
$\Rightarrow R=3r$
Now, initial potential of smaller sphere,
$V_1=\frac{1}{4}\pi {ϵ}_0\frac{Q}{r}$
$\therefore Q=V_{1}r\times 4\pi {ϵ}_0$
$\therefore$ Charge on $27$ spheres, we have
$Q_T=27\times 10\times r\times 4\pi {ϵ}_0$
Now, charge on bigger sphere
$Q_B=V_{2}R\times 4\pi {ϵ}_0$
Now, $Q_T=Q_B$
$\Rightarrow 270\times r\times 4\pi {ϵ}_0=V_{2}R\times 4\pi {ϵ}_0$
$\Rightarrow 270r=V_2\times 3r\Rightarrow V_2=90V$.