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Q.

A sphere A of radius 5 cm contains a charge of 120 nC. It is connected to two other spheres B and C having respective radii of 10 cm and 15 cm. Determine the charges on each of the spheres.

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a

20nC, 40nC, 60nC

b

20nC, 60nC, 40nC

c

20nC, 40nC, 10nC

d

20nC, 80nC, 20nC

answer is B.

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Detailed Solution

Charges are redistributed in the ratio of their capacities
$q_{1}^{'} : q_{2}^{'} : q_{3}^{'} = C_{1} : C_{2} : C_{3}$
For spherical capacitor
$\begin{array}{l} C_{1} : C_{2} : C_{3} = r_{1} : r_{2} : r_{3} = 1 : 2 : 3 \\ q_{1}^{'} = \frac{q}{6} = \frac{120}{6} = 20 nc; q_{2}^{'} = \frac{2 q}{6} = 40 nc \\ q_{3}^{'} = \frac{3 q}{6} = 60 nc \end{array}$

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