Q135 / 160 · AP EAMCET 2024 (18 May Shift 1) · Physics

216 small identical liquid drops each of surface area A coalesce to form a bigger drop. If the surface tension of the liquid is T, the energy released in the process is

  • A
    360 AT
  • Correct answer
    B
    180 AT
  • C
    90 AT
  • D
    120 AT

Solution

$\begin{aligned} & \mathrm{V}_{\mathrm{i}}=\mathrm{V}_{\mathrm{f}} \Rightarrow 216 \times \frac{4}{3} \pi \mathrm{r}^3=\frac{4}{3} \pi \mathrm{R}^3 \\ \therefore \quad & \mathrm{R}=\sigma \mathrm{r}\end{aligned}$ $\begin{aligned} & \therefore \quad \text { Energy released, } \mathrm{E}=216 \mathrm{AT}-4 \pi \mathrm{R}^2 \cdot \mathrm{~T} \\ & =216 \mathrm{AT}-4 \pi(6 \mathrm{r})^2 \cdot \mathrm{~T}\end{aligned}$ $\begin{aligned} & =216 \text { AT }-36 \mathrm{AT} \\ & =180 \mathrm{AT}\end{aligned}$

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

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