Vidaara.orgClass 11 · Physics
CodeVID-P11-09-SUR-01
Surface Tension — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
A free liquid drop tends to take a spherical shape because surface tension minimises its:
- A.volume
- B.surface area
- C.density
- D.pressure
2.
Surface energy per unit area is numerically equal to:
- A.the angle of contact
- B.the surface tension
- C.the density
- D.twice the surface tension
3.
The angle of contact for mercury on glass is:
- A.zero
- B.acute
- C.obtuse
- D.exactly $90^\circ$
4.
Capillary rise is greater in a tube that is:
- A.wider
- B.narrower
- C.longer
- D.shorter
5.
The excess pressure inside a liquid drop of radius $R$ is:
- A.$\frac{T}{R}$
- B.$\frac{2T}{R}$
- C.$\frac{4T}{R}$
- D.$\frac{2T}{R^2}$
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
Define surface tension and write its SI unit.
7.
Distinguish between cohesive and adhesive forces.
8.
Find the excess pressure in a water drop of radius $2\ \text{mm}$. (Take $T=0.072\ \text{N/m}$.)
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
Derive the expression for capillary rise $h=\frac{2T\cos\theta}{\rho g r}$.
10.
Why is the excess pressure in a soap bubble twice that in a liquid drop of the same radius?
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
Explain surface tension on the molecular level and define surface energy. Derive the formula for capillary rise and state why water rises but mercury is depressed in a glass tube.
Answer Key
Section A — Multiple Choice Questions
- (B) surface area
- (B) the surface tension
- (C) obtuse
- (B) narrower
- (B) $\frac{2T}{R}$
Section B — Short Answer (2 marks)
- Force per unit length acting along a liquid surface, $T=\frac{F}{L}$; SI unit N/m.
- Cohesive forces act between molecules of the same substance; adhesive forces act between molecules of two different substances.
- $P=\frac{2T}{R}=\frac{2\times0.072}{2\times10^{-3}}=72\ \text{Pa}$.
Section C — Short Answer (3 marks)
- The upward force from surface tension is $2\pi r T\cos\theta$; this supports the weight of the column $\pi r^2 h\rho g$. Equating gives $h=\frac{2T\cos\theta}{\rho g r}$.
- A soap bubble has two liquid–air surfaces (inner and outer) while a drop has only one, so the excess pressure $\frac{4T}{R}$ is double the drop's $\frac{2T}{R}$.
Section D — Long Answer (5 marks)
- Surface molecules have fewer neighbours, so a net inward pull makes the surface contract; surface energy is the work done per unit increase of area, equal to $T$. Balancing surface-tension force $2\pi r T\cos\theta$ against the column weight $\pi r^2 h\rho g$ gives $h=\frac{2T\cos\theta}{\rho g r}$. For water on glass $\theta$ is acute ($\cos\theta>0$) so it rises; for mercury $\theta$ is obtuse ($\cos\theta<0$) so it is depressed.
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