AP EAMCET · PHYSICS · Mechanical Properties of Fluids

Two mercury drops of radii \(\mathrm{r}\) and \(2 \mathrm{r}\) merge to form a bigger drop. The surface energy released in the process is nearly
(Surface tension mercury is \(\mathrm{S}\) and take \(9^{2 / 3}=4.326\) )

A \(1.6 \pi \mathrm{r}^2 \mathrm{~S}\)
B \(3.2 \pi \mathrm{r}^2 \mathrm{~S}\)
C \(17.1 \pi r^2 S\)
D \(2.7 \pi \mathrm{r}^2 \mathrm{~S}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(17.1 \pi r^2 S\)

Step-by-step Solution

Detailed explanation

Radii of drop, \(r_1=r\) and \(r_2=2 r\) Sum of volume of two drops = Volume of the bigger drop \[ \begin{aligned} & \frac{4}{3} \pi r^3+\frac{4}{3} \pi(2 r)^3=\frac{4}{3} \pi R^3 \\ & r^3+8 r^3=R^3 \\ & R^3=9 r^3=(9)^{1 / 3} r \end{aligned} \] Surface energy, \(E=4 \pi R^2 S\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Two mercury drops of radii \(\mathrm{r}\) and \(2 \mathrm{r}\) merge to form a bigger drop. The surface energy released in the process is nearly(Surface tension mercury is \(\mathrm{S}\) and take \(9^{2 / 3}=4.326\) )

Step-by-step Solution

Two mercury drops of radii \(\mathrm{r}\) and \(2 \mathrm{r}\) merge to form a bigger drop. The surface energy released in the process is nearly
(Surface tension mercury is \(\mathrm{S}\) and take \(9^{2 / 3}=4.326\) )