Question

Surface tension of mercury is $35\times$ 10${}^{-3}$ Nm${}^{-1}$ .The energy spent in spraying a drop of mercury of radius 1 cm into 1 million drops of equal size is ( in micro joule):

• A. 4356
• B. 4.356
• C. 43.56
• D. 0.4356

Answer 1

The correct option is A 4356

In this problem volume of mercury will be conserved.

So, initial volume is $\frac{4}{3}\pi (\frac{1}{100}{)}^3$
Final volume of 1,000,000 drops are 1,000,000 $\times \frac{4}{3}\pi (r{)}^3$
Equating $\frac{4}{3}\pi (\frac{1}{100}{)}^3=1,000,000\times \frac{4}{3}\pi (r{)}^3$
$\therefore r=\frac{1}{10000}m$

So, initial energy was $4\pi (\frac{1}{100}{)}^2\times 35\times {10}^{-3}$
final energy is $4\pi (\frac{1}{10000}{)}^2\times 35\times {10}^{-3}\times 1,000,000$

So, energy spent = final energy - initial energy
= $4\pi \times 35\times {10}^{-3}\left[\right(\frac{1}{10000}{)}^2\times 1,000,000-\left(\frac{1}{100}{)}^2\right]$
= 4.356 X ${10}^{-3}$ J
= 4356 $\mu J$ (1J = ${10}^6\mu J$)