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BITSAT 2021

Exam: BITSAT
Year: 2021
Subject: Physics
Chapter: Mechanical Properties of Fluids

BITSAT 2021 · Physics · Mechanical Properties of Fluids

A spherical drop of radius R is divided into eight equal droplets....

A spherical drop of radius

R

is divided into eight equal droplets. If surface tension is

\mathrm{T}

, then the work done in this process is

Options

A $2 \pi \mathrm{R}^{2} \mathrm{ T}$
B $3 \pi R^{2} T$
C $4 \pi R^{2} T$
D $2 \pi \mathrm{RT}^{2}$

Correct answer

C. $4 \pi R^{2} T$

Step-by-step solution

Volume of 8 small droplets = Volume of 1 big drop

\Rightarrow \frac{4}{3} \pi r^{3} \times 8=\frac{4}{3} \pi \mathrm{R}^{3} \Rightarrow r=\frac{\mathrm{R}}{(8)^{1 / 3}}

Work done

=(

Change in area

) \times

surface tension

=\left(4 \pi r^{2} n-4 \pi \mathrm{R}^{2}\right) \mathrm{T}\left\{4 \pi\left(\frac{\mathrm{R}^{2}}{(8)^{2 / 3}}\right) \times 8-4 \pi \mathrm{R}^{2}\right\} \mathrm{T}=4 \pi \mathrm{R}^{2} \mathrm{ T}

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