Question

The diameter of one drop of water is $0.2cm$. The work done in breaking one drop into 100 droplets will be:

• A. $7.9\times 10^{-6}J$
• B. $5.92\times 10^{-6}J$
• C. $2.92\times 10^{-6}J$
• D. $1.92\times 10^{-6}J$

Answer 1

Answer: (A)

Let $R$ and $r$ be the radii of big drop and each smaller drop.
$\therefore$ Volume of big drop
$=$ volume of smaller drops
$\frac{4}{3}\pi R^3=1000\times \frac{4}{3}\times r^3$
$\Rightarrow r=\frac{R}{10}=\frac{0.1\times 10^{-2}}{10}$
$=0.01\times 10^{-2}m$
$\left(\because R=0.1\times 10^{-2}m\right)$
$\therefore r=1\times 10^{-4}m$
The work done in breaking the big drop into $1000$ small droplets is
$W=T\left(1000\times 4\pi r^2-4\pi R^2\right)$
$=T\times 4\pi \left(1000\times 10^{-8}-10^{-6}\right)$
$=4\pi T\times 10^{-6}(10-1)$
$=4\pi T\times 10^{-6}\times 9$
$=36\times 3.14\times 7\times 10^{-2}\times 10^{-6}$
$=7.9\times 10^{-6}J$