Question

The surface tension of water in contact with air at ${18}^{\circ }\text{C}$ is $0.073\text{N/m}$. The pressure inside a droplet of water is to be $0.02{\text{N/cm}}^2$ greater than the outside pressure. Calculate the diameter of the droplet of water.

• A. $0.73\text{mm}$
• B. $1.47\text{mm}$
• C. $1.45\text{mm}$
• D. $1.46\text{mm}$

Answer 1

The correct option is D $1.46\text{mm}$

Given that,
Surface tension ($\sigma$) $=0.073\text{N/m}$
Excess pressure inside droplet $P=0.02{\text{N/cm}}^2=0.02\times {10}^4{\text{N/m}}^2$
Let $d$ be the diameter of droplet.
We know that $P=\frac{4\sigma }{d}$
$\Rightarrow d=\frac{4\sigma }{P}=\frac{4\times 0.073}{0.02\times {10}^4}=0.00146\text{m}$
​​​​​ $\Rightarrow d=1.46\text{mm}$