Q146 / 160 · AP EAMCET 2024 (21 May Shift 1) · Physics

Eight drops of mercury of equal radii and possessing equal charge combine to form a big drop. If the capacity of each drop is ' C '. then capacity of the big drop is

  • A
    4 C
  • Correct answer
    B
    2 C
  • C
    8 C
  • D
    16 C

Solution

Volume of big drop $=8 \times$ volume of small drop $\Rightarrow \frac{4}{3} \pi R^3=8 \times \frac{4}{3} \pi r^2 \Rightarrow R=2 r$ $\therefore \quad$ Capacity of big drop, $\mathrm{C}^{\prime}=4 \pi \varepsilon_0 \mathrm{R}=4 \pi \varepsilon_0(2 \mathrm{r})=2\left(4 \pi \varepsilon_0 \mathrm{r}\right)=2 \mathrm{C}$

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

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