Surface tension, angle of contact and capillary rise — practice questions

Question 1 · difficulty L2 · understanding

Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is $\_\_\_\_$ - ( $S$ is the surface tension of mercury).

• A. $8 \pi r^2 \mathrm{~S}$
• B. $16 \pi r^2 S$
• C. $64 \pi r^2 S$
• D. $4 \pi r^2 \mathrm{~S}$

Question 2 · difficulty L2 · understanding

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $\alpha \pi \times 10^{-4}$ J. The value of $\alpha$ is _________. (Take $\pi = 3.14$)

• A. 0.86
• B. 0.64
• C. 1.92
• D. 7.68

Question 3 · difficulty L2 · understanding

Given below are two statements : Statement I : Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid. Statement II : Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension. In the light of the above statements, choose the correct answer from the options given below

• A. Statement I is false but Statement II is true
• B. Statement I is true but Statement II is false
• C. Both Statement I and Statement II are false
• D. Both Statement I and Statement II are true

Question 4 · difficulty L2 · understanding

Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. B. As the temperature of liquid rises, the coefficient of viscosity increases. C. As the temperature of gas increases, the coefficient of viscosity increases D. The onset of turbulence is determined by Reynold's number. E. In a steady flow two stream lines never intersect. Choose the correct answer from the options given below:

• A. B, C, D Only
• B. C, D, E Only
• C. A, D, E Only
• D. A, B, C Only

Question 5 · difficulty L2 · understanding

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

• A. $$1: 9$$
• B. $$1: 27$$
• C. $$1: 81$$
• D. $$1: 3$$

Question 6 · difficulty L2 · understanding

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $$\mathrm{R}=$$ Radius of bubble, $$\mathrm{S}=$$ Surface tension of bubble)

• A. $$\frac{S}{R}$$
• B. $$\frac{4 \mathrm{~S}}{\mathrm{R}}$$
• C. $$\frac{4 \mathrm{R}}{\mathrm{S}}$$
• D. $$\frac{2 S}{R}$$

Question 7 · difficulty L2 · understanding

Given below are two statements: Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given below

• A. Both Statement I and Statement II are false
• B. Both Statement I and Statement II are true
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Question 8 · difficulty L2 · understanding

Given below are two statements : Statement (I) :Viscosity of gases is greater than that of liquids. Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Statement I is correct but statement II is incorrect
• B. Statement I is incorrect but Statement II is correct
• C. Both Statement I and Statement II are incorrect
• D. Both Statement I and Statement II are correct

Question 9 · difficulty L2 · understanding

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $$\mathrm{A}$$ is $$1.5 \mathrm{~cm}^{2}$$, and $$\mathrm{B}$$ is $$25 \mathrm{~mm}^{2}$$, if the speed of liquid at $$\mathrm{B}$$ is $$60 \mathrm{~cm} / \mathrm{s}$$ then $$\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}\right)$$ is : (Given $$\mathrm{P}_{\mathrm{A}}$$ and $$\mathrm{P}_{\mathrm{B}}$$ are liquid pressures at $$\mathrm{A}$$ and $$\mathrm{B}$$% points. density $$\rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$$ $$\mathrm{A}$$ and $$\mathrm{B}$$ are on the axis of tube

• A. $$27 \mathrm{~Pa}$$
• B. $$175 \mathrm{~Pa}$$
• C. $$135 \mathrm{~Pa}$$
• D. $$36 \mathrm{~Pa}$$

Question 10 · difficulty L2 · understanding

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $$5 \mathrm{~cm}$$. If the tube is dipped in a similar manner in another liquid $$\mathrm{B}$$ of surface tension and density double the values of liquid $$\mathrm{A}$$, the height of liquid column raised in liquid $$\mathrm{B}$$ would be __________ m.

• A. 0.05
• B. 0.20
• C. 0.5
• D. 0.10