A spherical drop of potential 2.5 V is forme | vedclass

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(C) Let the radius of each small drop be $r$ and its charge be $q$. The potential of a small drop is $V_s = \frac{kq}{r} = 2.5 \ V$.When $n = 125$ sma

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$62.5$

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(C) Let the radius of each small drop be $r$ and its charge be $q$. The potential of a small drop is $V_s = \frac{kq}{r} = 2.5 \ V$.When $n = 125$ small drops combine to form a large drop of radius $R$,the volume remains conserved.So,$\frac{4}{3} \pi R^3 = n \cdot \frac{4}{3} \pi r^3$,which gives $R^3 = n r^3$,or $R = n^{1/3} r$.For $n = 125$,$R = (125)^{1/3} r = 5r$.The total charge of the large drop is $Q = nq = 125q$.The potential of the large drop is $V_L = \frac{kQ}{R} = \frac{k(nq)}{n^{1/3}r} = n^{2/3} V_s$.Substituting the values: $V_L = (125)^{2/3} 	imes 2.5 = (5^3)^{2/3} 	imes 2.5 = 5^2 	imes 2.5 = 25 	imes 2.5 = 62.5 \ V$.

$A$ spherical drop of potential $2.5 \ V$ is formed from $125$ identical small drops. Find the potential of the large drop in $V$.

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