Question
Derive an expression for the excess pressure inside a liquid drop.
✓
Answer
Consider a liquid drop of radius r. If one tries to enhance the radius by a small amount ‘dr’ work has to be done to overcome the excess pressure (P). 
Work done $=\text{dW}=\text{p}\times4\pi\text{r}^2\times\text{dr}$ Due to surface tension $'\sigma',$ the excess pressure exists. The work done to change the area is also written as,
Work done $=\text{dW}=\text{p}\times4\pi\text{r}^2\times\text{dr}$ Due to surface tension $'\sigma',$ the excess pressure exists. The work done to change the area is also written as, $\text{dW}=\sigma \times\text{change in area}$
$=\sigma\times4\pi\{(\text{r}+\text{dr})^2-\text{r}^2\}=\sigma8\pi\text{rdr}$
$\therefore\text{P}4\pi\text{r}^2\text{dr}=\sigma8\pi\text{r}\text{ dr}$
$\therefore\text{P}=\frac{2\sigma}{\text{r}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A constant torque is acting on a wheel. If starting from rest, the wheel makes n rotations in t seconds, show that the angular acceleration is given by $\alpha=\frac{4\pi\text{n}}{\text{t}^2}\text{rad}{\text{ s}}^{-2}$
→Prove that the angular momentum of a single particle moving with a constant velocity around a point remains constant throughout its motion.(NCERT)
How many types of inertia are there? Explain by example.
Name one system where the compressional and tensional modulus of elasticity are different. Give reason.
What is wave? Mention those two properties of the medium due to which transmission of mechanical waves is possible in the medium?
Two monoatomic ideal gases 1 and 2 of molecular masses $m_1$ and $m_2$ respectively are enclosed in separate containers kept at the same temperature. What is the ratio of the speed of sound in gas 1 to that in gas 2 ?
→The length and the radius of a cylinder measured with a slide callipers are found to be 4.54cm and 1.75cm respectively. Calculate the volume of the cylinder.
Consider a pair of identical pendulums, which oscillate with equal amplitude independently such that when one pendulum is at its extreme position making an angle of 2° to the right with the vertical, the other pendulum makes an angle of 1° to the left of the vertical. What is the phase difference between the pendulums?
A Carnot engine is operating between 600K and 200K. Consider that the actual energy produced is 2 kJ per kilocalorie of heat absorbed. Compare the real efficiency with the efficiency of Carnot engine.
Is the bulb of a thermometer made of diathermic or adiabatic wall?