Q105 / 150 · MHT CET 2021 (20 Sep Shift 1) · Physics

The surface energy of a liquid drop is ' $U$ '. It splits up into 512 equal droplets. The surface energy becomes

  • Correct answer
    A
    $8 \mathrm{U}$
  • B
    $6 \mathrm{U}$
  • C
    $4 \mathrm{U}$
  • D
    $2 \mathrm{U}$

Solution

$\begin{aligned} & \frac{4}{3} \pi R^3=512 \times \frac{4}{3} \pi r^3 \\ & \therefore r=\frac{R}{8} \\ & U=4 \pi R^2 T \\ & U^{\prime}=512 \times 4 \pi r^2 T \\ & =512 \times \frac{4 \pi R^2 T}{64}=8\left(4 \pi R^2 T\right)=8 U\end{aligned}$

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

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