## Properties Of Bulk Matter

## Viscosity And Surface Tension Multiple Correct Answers Type Questions

**Question 1. A spherical steel ball released at the top of a long column of glycerin of length L falls through a distance L/2 with accelerated motion and the remaining distance L/2 with a uniform velocity. If t _{1} and t_{2} denote the times taken to cover the first and second half and W_{1} and W_{2} the work done against gravity in the two halves, then**

- t
_{1}< t_{2}; W_{1 }> W_{2} - t
_{1}> t_{2}; W_{1}< W_{2} - t
_{1}= t_{2}; W_{1}= W_{2} - t
_{1}> t_{2}; W_{1}= W_{2}

**Answer:** 4. t_{1} > t_{2}; W_{1} = W_{2}

**Question 2. Falling raindrops acquire terminal velocity due to**

- Upthrust of air
- Viscous force of air
- Surface tension
- Air current in the atmosphere

**Answer:** 2. Viscous force of air

**Question 3. An iron ball and an aluminum ball of equal diameters are released from the upper surface of the water of a deep lake. The bottom of the lake is reached by**

- The aluminum ball earlier
- The iron ball earlier
- Both the balls at the same time
- The iron ball only—the aluminum ball will never reach the bottom.

**Answer:** 2. The iron ball earlier

**Question 4. When a small lead shot is released from the upper surface of a viscous liquid,**

- The lead shot will go on descending with an acceleration g
- The velocity of the lead shot will decrease with time
- The velocity of the lead shot will increase with time
- After some time, the lead- ’shot will acquire a uniform velocity

**Answer:** 4. After some time, the lead- ’shot will acquire a uniform velocity

**Question 5. A spherical ball is falling with a uniform velocity v through a viscous medium of coefficient of viscosity η. If the viscous force acting on the spherical ball is F then**

- \(F \propto \eta and F \propto \frac{1}{\nu}\)
- \(F \propto \eta and F \propto \nu\)
- \(F \propto \frac{1}{\eta} and F \propto \frac{1}{v}\)
- \(F \propto \frac{1}{\eta} and F \propto v\)

**Answer:** 2. \(F \propto \eta and F \propto \nu\)

**Question 6. The velocity of efflux of a liquid through an orifice does not depend on**

- Acceleration due to gravity
- Height of the liquid in the vessel
- Density of the liquid
- Viscosity of the liquid

**Answer:** 3. Density of the liquid

**Question 7. The ratio of the terminal velocities of two water drops, when they fall towards the earth’s surface, is 4 : 9. The ratio of their radii is**

- 4:9
- 2:3
- 3:2
- 9:4

**Answer:** 2. 2:3

**Question 8. In case of a falling body of radius r through a viscous medium with a terminal velocity y,**

- v ∝ r
- v ∝ r
^{-2} - v ∝ r
^{-1} - v ∝ r²

**Answer:** 4. v ∝ r^{2}

**Question 9. A small spherical ball of radius r falls freely under gravity through a distance h before entering a tank of water. If, after entering the water, the velocity of the ball does not change, then h is proportional to**

- r
^{2} - r
^{3} - r
^{4} - r
^{5}

**Answer:** 3. r^{4}

**Question 10. A small metal sphere of radius r and density ρ falls from rest in a viscous liquid of density σ and coefficient of viscosity η. Due to friction heat is produced. The rate of production of heat when the sphere has acquired the terminal velocity is proportional to**

- r
^{2} - r
^{3} - r
^{4} - r
^{5}

**Answer:** 4. r^{5}

**Question 11. If a fluid flows through the narrower region of a tube of non-uniform cross-section, then in that region of the tube**

- Both the velocity and the pressure of the fluid will increase
- Both the velocity and the pressure of the fluid will decrease
- Velocity of the fluid will decrease but pressure will increase
- Velocity of the fluid will increase but pressure will decrease

**Answer:** 4. Velocity of the fluid will increase but pressure will decrease

**Question 12. Working principle of a sprayer or atomizer depends on**

- Bernoulli’s principle
- Boyle’s law
- Archimedes’ principle
- Newton’s laws of motion.

**Answer:** 1. Bernoulli’s principle

**Question 13. An incompressible fluid flows through a tube at a uniform rate. Radius of the tube at a point A is 2 r and that at a point B is r. If the velocity at the point A is v, then velocity at the point B will be**

- 2v
- y
- v/2
- 4v

**Answer:** 4. 4v

**Question 14. For a uniform flow of an incompressible, non-viscous fluid Bernoulli’s theorem expresses,**

- Conservation Of Angular Momentum
- Conservation Of Density
- Conservation Of Momentum
- Conservation Of Energy

**Answer:** 4. Conservation Of Energy

**Question 15. For a streamline flow, if the elevation head is h, then velocity head and pressure head will be**

- \(\frac{1}{2} \nu^2 and \frac{P}{\rho}\)
- \(\frac{1}{2} \frac{v^2}{g} and \frac{P}{\rho g}\)
- \(\frac{1}{2} \frac{v^2}{g} and \frac{P}{\rho}\)
- \(\frac{1}{2} v^2 and \frac{P}{\rho g}\)

**Answer:** 2. \(\frac{1}{2} \frac{v^2}{g} and \frac{P}{\rho g}\)

**Question 16. Water flows through a tube of non-uniform cross-section. Cross-sectional areas at parts A, B, and C of the tube are 25 cm², 5 cm², and 35 cm² respectively. In which part does the speed of water become maximum?**

- A
- B
- C
- Equal speed at all parts

**Answer:** 2. B

**Question 17. A cylinder of length 20 m is filled completely with water. Velocity of efflux of water through an orifice on the wall of the cylinder near its base is [g = 10 m • s ^{-2}]**

- 10 m · s
^{-1} - 20m · s
^{-1} - 25.5m · s
^{-1} - 5m · s
^{-1}

**Answer:** 2. 20 m · s^{-1}

**Question 18. Two metallic spheres of radii a _{1} and a_{2} are falling freely through a viscous medium. The ratio of their terminal velocities will be**

- \(\frac{a_1}{a_2}\)
- \(\frac{a_2}{a_1}\)
- \(\frac{a_1^2}{a_2^2}\)
- \(\frac{a_2^2}{a_1^2}\)

**Answer:** 3. \(\frac{a_1^2}{a_2^2}\)

**Question 19. A large container (with open top) of negligible mass and uniform cross-sectional Area A has a small hole of cross sectional area a in its side wall near the bottom. The container is kept on a smooth horizontal platform and contains a liquid of density ρ and mass m. If the liquid starts flowing out of the hole at time t = 0, the initial acceleration of the container is**

- \(\frac{g a}{A}\)
- \(\frac{g A}{a}\)
- \(\frac{2 g a}{A}\)
- \(\frac{g A}{2 a}\)

**Answer:** 3. \(\frac{2 g a}{A}\)

**Question 20. The velocity of the liquid when 75% of the liquid has drained out is**

- \(\sqrt{\frac{3 m g}{4 A \rho}}\)
- \(\sqrt{\frac{2 m g}{A \rho}}\)
- \(2 \sqrt{\frac{m g}{A \rho}}\)
- \(\sqrt{\frac{m g}{2 A \rho}}\)

**Answer:** 4. \(\sqrt{\frac{m g}{2 A \rho}}\)

**Question 21. The property of liquid lead utilised in making lead shots is**

- Expansion of liquid lead on solidification
- Specific gravity of liquid lead
- Compressibility of liquid lead
- Surface tension of liquid lead

**Answer:** 4. Surface tension of liquid lead

**Question 22. Surface energy of a water drop of radius r will be directly proportional to**

- r
^{3} - r
^{2} - r
- 1/r

**Answer:** 4. 1/r

**Question 23. The energy required to convert a large water drop of radius R into n smaller droplets of water, each having radius r, is [S = surface tension of water]**

- \(\left(4 \pi r^2 n-4 \pi R^2\right) S\)
- \(\left(\frac{4}{3} \pi r^3 \cdot n-\frac{4}{3} \pi R^2\right) S\)
- \(\left(4 \pi R^2-4 \pi r^2\right) n S\)
- \(\left(4 \pi R^2-n \cdot 4 \pi r^2\right) S\)

**Answer:** 1. \(\left(4 \pi r^2 n-4 \pi R^2\right) S\)

**Question 24. Small liquid drops take the spherical shape because of**

- Adhesion
- Gravitational force
- Equal pressure from all directions
- Surface tension.

**Answer:** 4. Surface tension.

**Question 25. When a vertical capillary tube is dipped into a liquid, then the liquid level inside the tube rises or falls a little from the level outside the tube. The reason behind this is**

- Viscosity of the liquid
- Surface tension of the liquid
- Diffusion
- Osmosis

**Answer:** 2. Surface tension of the liquid

**Question 26. A solid substance is dipped in a liquid and then brought out of it. It is seen that some liquid sticks to the surface of the solid. The angle of contact between the solid and the liquid is**

- Equal to 90°
- More than 90°
- Less than 90°
- Equal to 135°

**Answer:** 3. Less than 90°

**Question 27. In an experiment on surface tension, water rises up to a height of 0.1 m in a capillary tube. If that experiment is performed inside an artificial satellite revolving a round the earth then water will rise in the capillary tube by**

- 0.1m
- 0.2 m
- 0.98 m
- Entire length of the tube

**Answer:** 4. Entire length of the tube

**Question 28. If a number of capillary tubes of different radii (r) are immersed in water, then water rises in the tubes through different heights (h). Then**

- h/r² = constant
- h/r = constant
- hr = constant
- hr² = constant

**Answer:** 3. hr = constant

**Question 29. Water rises up to a height of h in a certain capillary tube of a particular diameter. Another identical capillary tube is taken whose diameter is half that of the previous tube. The height up to which water will rise in this tube is**

- 4h
- 3h
- 2h
- h

**Answer:** 3. 2h

**Question 30. If surface tension of water is 0.06 N · m ^{-1}, then the height up to which water (θ = 0) will rise in a capillary tube of diameter 1 mm will be**

- 1.22 cm
- 2.45 cm
- 3.12 cm
- 3.86 cm

**Answer:** 2. 2.45 cm

**In this type of question, more than one options are correct.**

**Question 31. Excess pressure can be \(\left(\frac{2 T}{R}\right)\) for**

- Spherical drop
- Spherical meniscus
- Cylindrical bubble in air
- Spherical bubble in water

**Answer:**

1. Spherical drop

2. Spherical meniscus

4. Spherical bubble in water

**Question 32. Viscous force is somewhat like friction as it opposes the motion and is nonconservative but not exactly so, because**

- It is velocity-dependent while friction not
- It is velocity independent while friction is not
- It is temperature-dependent while friction is not
- It is independent of area like surface tension while friction depends on area

**Answer:**

1. It is velocity dependent while friction not

3. It is temperature dependent while friction is not

**Question 33. If the liquid rises to the same height in two capillaries of the same material at the same temperature**

- The weight of liquid in both capillaries must be equal
- The radius of meniscus must be equal
- The capillaries must be cylindrical and vertical
- The hydrostatic pressure at the base of the capillaries must be same

**Answer:**

1. The weight of liquid in both capillaries must be equal

2. The radius of meniscus must be equal

4. The hydrostatic pressure at the base of the capillaries must be same

**Question 34. n drops of a liquid, each with surface energy E, join to form a single drop. Then**

- Some energy will be released in the process
- Some energy will be absorbed in the process
- The energy released will be E(n- n
^{2/3}) - The energy absorbed will be nE(2
^{2/3}– 1)

**Answer:**

1. Some energy will be released in the process

3. The energy released will be E(n- n^{2/3})

**Question 35. The velocity of efflux of an ideal liquid does not depend on**

- The area of orifice
- The density of liquid
- The area of cross section of the vessel
- The depth of the point below the free surface of the liquid

**Answer:**

- The area of orifice
- The density of liquid
- The area of cross-section of the vessel

**Question 36. A syringe containing water is held horizontally with its nozzle at a height, h = 1.25 m above the ground as shown in Fig. The diameter of the piston is 5 times that of the nozzle. The piston is pushed with a constant speed of 20 cm · s ^{-1}. If g = 10 m · s^{-2}**

- The speed of water emerging from the nozzle is 5 m · s
^{-1} - The time taken by water to hit the ground is 0.5s
- The horizontal range, R = 2.5m
- The magnitude of the velocity with which the water hits the ground is 5√2m · s
^{-1}

**Answer:** All are correct

**Question 37. A liquid of density ρ is contained in a cylindrical vessel of radius r. When the vessel is rotated about its axis at an angular velocity ω, the liquid rises by h at the sides as shown in Fig. If p _{c} is the pressure of the liquid at the centre and p_{s} at the sides of the vessel, then**

- \(p_c>p_s\)
- \(p_c<p_s\)
- \(h=\frac{r^2 \omega^2}{2 g}\)
- \(h=\frac{r^2 \omega^2}{g}\)

**Answer:**

1. \(p_c>p_s\)

3. \(h=\frac{r^2 \omega^2}{2 g}\)

**Question 38. A container of width 2 a is filled with a liquid. A thin wire of mass per unit length μ is gently placed on the middle of the surface. So the liquid surface is depressed by a distance y. The surface tension of liquid is given by**

- \(\sigma=\frac{\mu g}{2 \cos \theta}\)
- \(\sigma=\frac{\mu g}{2 \sin \theta}\)
- \(\sigma=\frac{\mu g a}{2 y}, if y \ll a \)
- \(\sigma=\frac{\mu g a}{y}, if y \ll a\)

**Answer:**

2. \(\sigma=\frac{\mu g}{2 \sin \theta}\)

3. \(\sigma=\frac{\mu g a}{2 y}, if y \ll a \)