Question

The diameter of one drop of water is $0.2\, cm$. 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) $
$=T \times 4 \pi\left(1000 \times 10^{-8}-10^{-6}\right)$
$=4 \pi T \times 10^{-6}(10-1)$
$=4 \pi T \times 10^{-6} \times 9$
$=36 \times 3.14 \times 7 \times 10^{-2} \times 10^{-6}$
$=7.9 \times 10^{-6} \,J$