Q88 / 100 · BITSAT 2024 (Memory Based Paper 3) · Physics

The potential of a large liquid drop when eight liquid drops are combined is 20 V , then the potential of each single drop was

  • A
    10 V
  • B
    7.5 V
  • Correct answer
    C
    5 V
  • D
    2.5 V

Solution

Volume of eight drops = Volume of a big drop $\therefore \quad\left(\frac{4}{3} \pi r^3\right) \times 8=\frac{4}{3} \pi R^3$ $\Rightarrow \quad 2 r=R$...(i) According to charge conservation, $8 q=Q$...(ii) Potential of one small drop, $V^{\prime}=\frac{q}{4 \pi \varepsilon_0 r}$ Similarly, potential of big drop, $V=\frac{Q}{4 \pi \varepsilon_0 R}$ Now, $\quad \frac{V^{\prime}}{V}=\frac{q}{Q} \times \frac{R}{r}$ $\Rightarrow \quad \frac{V^{\prime}}{20}=\frac{q}{8 q} \times \frac{2 r}{r} \quad$ [from Eqs. (i) and (ii)] $\therefore \quad V^{\prime}=5 \mathrm{~V}$

Hence, the correct answer is option: 'C'.

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