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(D) Let the radius of each small droplet be $r$ and its charge be $q$. The potential of a small droplet is $v = \frac{kq}{r}$.When $n = 125$ droplets

Vedclass · Accepted Answer

$0.1$

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(D) Let the radius of each small droplet be $r$ and its charge be $q$. The potential of a small droplet is $v = \frac{kq}{r}$.When $n = 125$ droplets merge to form a large drop of radius $R$ and charge $Q$,the total charge is conserved: $Q = nq = 125q$.The volume is also conserved: $\frac{4}{3}\pi R^3 = n \cdot \frac{4}{3}\pi r^3$,which implies $R^3 = nr^3$,or $R = n^{1/3}r$.For $n = 125$,$R = (125)^{1/3}r = 5r$.The potential of the large drop is $V = \frac{kQ}{R} = \frac{k(nq)}{n^{1/3}r} = n^{2/3} \left(\frac{kq}{r}\right) = n^{2/3}v$.Given $V = 2.5\, V$ and $n = 125$,we have $2.5 = (125)^{2/3}v$.$2.5 = (5^3)^{2/3}v = 5^2 v = 25v$.Therefore,$v = \frac{2.5}{25} = 0.1\, V$.

$A$ spherical drop of mercury having a potential of $2.5\, V$ is obtained as a result of merging $125$ droplets. The potential of constituent droplets would be........$V$

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