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KCET2021PhysicsCapacitance

Eight drops of mercury of equal radii combine to form a big drop. The capacitance of a bigger drop as compared to each smaller drop is

Options

  1. A2 times
  2. B8 times
  3. C4 times
  4. D16 times

Correct answer

A. 2 times

Step-by-step solution

Let R and r be the radii of bigger and each smaller drop, respectively. Volume of bigger drop =8 Volume of smaller drop 4 3 R³=8 4 3 r³ or R=2 r...(i) As, capacitance of a smaller spherical drop is aligned C &=4 ₀ r C & r aligned So, C_ bigger C_ smaller = r_ bigger r_ smaller = R r = 2 r r =2 [using Eq. (i)] So, capacitance of bigger drop is two times as compared to each smaller drop.

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