There are 27 drops of a conducting fluid. Each has a radius r and they are charged to a potential V0. These are combined to form a bigger drop. Its potential will be:
Correct answer: C. 9V0
- A. V0
- B. 3V0
- C. 9V0
- D. 27V0
Explanation
When the 27 smaller drops are combined, the volume of the larger drop is the sum of the volumes of the smaller drops. If each drop has a radius r, the volume of each drop is proportional to r3. The total volume of the larger drop is thus 27 r3. The new radius R of the larger drop is such that R3 = 27r3, so R = 3r.The potential of a conducting sphere is proportional to its charge divided by its radius. Since the charge is conserved, and the radius of the larger drop is 3 times that of the smaller drops, the new potential V is V = 9V0.Option A is incorrect because the potential does not remain the same after combining.Option B is incorrect because the potential does not scale linearly with the radius increase by a factor of 3.Option D is incorrect because while the total charge is 27 times that of a single drop, the potential depends on the new radius, not just the total charge.
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