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A large hollow metal sphere of radius R has a small opening at the top. Small drops of mercury, each of radius r and charged to a potential V , fall into the sphere. The potential of the sphere becomes V' after N drops fall into it. Then

Options

  1. AV ′ = V for any value of N
  2. BV ′ = V for N = R r 2 / 3
  3. CV ′ = V for N = R r 1 / 3
  4. DV ′ = V for N = R r

Correct answer

C. V ′ = V for N = R r 1 / 3

Step-by-step solution

V = k q r After N d r o p p o t e n t i a l o f h o l l o w s p h e r e = V ′ V ′ = k N q R V ′ = V ⇒ k q r = k N q R ⇒ N = R r

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