MHT CET · Physics · Mechanical Properties of Fluids

A liquid drop having surface energy $E$ is spread into $512$ droplets of the same size. The final surface energy of the droplets is

A $2 E$
B $4 E$
C $8 E$
D $12 E$

Verified Solution

Answer & Solution

Correct Answer

(C) $8 E$

Step-by-step Solution

Detailed explanation

The surface area of the liquid drop is

A = 4 π R^{2}

Its surface energy is

E

When the drop splits in

512

droplets, the surface area of each droplet is

4 π r^{2}

∴

Total surface area

A_{2}

= 512 \times 4 π r^{2}

The volume of the bigger drop is

\frac{4}{3} π R^{3}

and the volume of small droplets is

512 \times \frac{4}{3} π r^{3}

∴ \frac{4}{3} π R^{3} = 512 \times \frac{4}{3} π r^{3} \Rightarrow r = \frac{R}{8}

∴ A_{2} = 512 \times 4 π r^{2} = 512 \times 4 π {(\frac{R}{8})}^{2} = 8 A_{1}

Surface energy

E = A . T

(

T

is surface tension and

A

is area)

∴ \frac{E_{n}}{E_{0}} = \frac{A_{2} \cdot T}{A_{1} \cdot T} = \frac{8 \cdot A_{1}}{A_{1}} = 8

∴ E_{n} = 8 E

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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A liquid drop having surface energy E is spread into 512 droplets of the same size. The final surface energy of the droplets is

Step-by-step Solution

A liquid drop having surface energy $E$ is spread into $512$ droplets of the same size. The final surface energy of the droplets is