NCERT Exemplar Solutions Class 11 Physics Mechanical Properties of Fluids — Multiple Choice Questions Q1–10

NCERT Exemplar Problems, Class 11 Physics — Mechanical Properties of Fluids, MCQ I and MCQ II. All 10 questions solved.

The book numbers these questions 10.1 to 10.10 (the exemplar’s Unit 10 is Chapter 9 of the current NCERT textbook); here they are Questions 1 to 10. Questions 1 to 5 are MCQ I (exactly one option is correct) and Questions 6 to 10 are MCQ II (one or more options may be correct). Four ideas carry the whole page:

• Viscous drag grows with speed. A body falling through a viscous liquid speeds up until the drag and buoyancy balance its weight, and then moves at a constant terminal velocity.
• Streamlines and continuity. In steady flow streamlines never cross, and the speed in a pipe varies inversely as the cross-sectional area, $Av = \text{constant}$.
• Archimedes’ principle. A floating body displaces its own weight of liquid; a sunken body displaces only its own volume.
• Surface molecules. A molecule at the surface has fewer neighbours, so it has higher potential energy than one inside; that excess is the surface energy.

Key insight. Several options here describe a true-sounding picture that answers a different question. In Question 6 the net force on a surface molecule at rest must be zero, whatever the cohesive pull; in Question 8 a coin on the block displaces more water than the same coin on the floor.

Choose the correct answer from the given options. (MCQ I: one correct. MCQ II: one or more correct.)

Question 1

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in Fig. 10.1, indicate the one that represents the velocity ($v$) of the pebble as a function of time ($t$).

Solution. At the start the pebble is at rest, so there is no viscous drag and it accelerates under its weight less the buoyant force. As it speeds up, the viscous drag (proportional to $v$ by Stokes’ law) grows, so the net force and the acceleration fall continuously. The slope of the $v$–$t$ graph therefore starts at its largest value and decreases smoothly towards zero as $v$ approaches the terminal velocity. Graph (a) has constant acceleration (no drag), (b) has the pebble waiting before it moves, and (d) has a sudden jump from constant acceleration to zero acceleration, which would need the drag to switch on abruptly. Only (c) rises steeply at first and flattens gradually.

Question 2

Which of the following diagrams (Fig. 10.2) does not represent a streamline flow?

Solution. A streamline is drawn so that its tangent at every point gives the direction of the fluid’s velocity there. In steady flow each point has only one velocity, so two streamlines can never cross: at a crossing point the fluid would have to move in two directions at once. In (a), (b) and (c) the lines bend, spread or converge, but none of them cross, so each is a possible streamline pattern. In (d) two lines cut across the others, so that pattern cannot be streamline flow.

Question 3

Along a streamline

Solution. Streamline (steady) flow means that the velocity at each fixed point does not change with time: every particle that passes a given position passes it with the same velocity. That is statement (b). It says nothing about a single particle keeping its velocity as it moves along: where the streamline bends, the direction changes, and where the streamlines crowd together (a narrower tube), the speed rises. So (a) and (d) are false, and (c) is false because particles at different points along the same streamline generally have different velocities.

Question 4

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes is

Solution. An ideal fluid is incompressible, so the same volume passes every section per second: $A_1v_1 = A_2v_2$. The area goes as the square of the diameter, so

$$\frac{v_1}{v_2} = \frac{A_2}{A_1} = \left(\frac{d_2}{d_1}\right)^2 = \left(\frac{3.75}{2.5}\right)^2 = (1.5)^2 = \frac{9}{4}.$$

The fluid moves faster in the narrower (2.5 cm) section. Option (b) is the ratio of the diameters, which forgets that area goes as $d^2$.

Question 5

The angle of contact at the interface of water–glass is $0^\circ$, ethyl alcohol–glass is $0^\circ$, mercury–glass is $140^\circ$ and methyl iodide–glass is $30^\circ$. A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is

Solution. The meniscus is concave (curving down in the middle) when the angle of contact is acute, because the liquid’s adhesion to the glass pulls it up the walls. It is convex (bulging up in the middle) when the angle of contact is obtuse, because cohesion dominates and the liquid pulls away from the glass. Of the four, only mercury has an obtuse angle, $140^\circ > 90^\circ$. Water and ethyl alcohol ($0^\circ$) and methyl iodide ($30^\circ$) all give concave menisci.

Question 6

For a surface molecule

Solution. Energy. A molecule inside the liquid is surrounded on all sides by neighbours, and each attractive bond lowers its potential energy. A molecule at the surface has neighbours only on one side, so it has fewer bonds and a higher (less negative) potential energy. Bringing a molecule from the inside to the surface therefore costs energy, and that is exactly why a liquid surface has surface energy and tends to contract. So (d) is true and (c) is false.

Force. The surface of a liquid at rest is not moving, so every molecule in it is in equilibrium and the net force on it is zero: (a). The textbook’s picture of a “net inward pull” on a surface molecule counts only the attractive forces from the molecules below. When the surface layer is in equilibrium, that pull is balanced by the short-range repulsion from the molecules beneath, so (b) does not describe the total force.

Question 7

Pressure is a scalar quantity because

Solution. Pressure is defined from the force acting normal to a surface: $P = F_\perp/A$. Whatever the orientation of the small area at a point, a fluid at rest pushes on it perpendicularly with the same force per unit area, so pressure has a magnitude but no direction of its own; the direction belongs to the surface it acts on. That is (c). It is also an intensive quantity: halving the area halves the normal force, so the ratio is independent of the size of the area chosen, which is (d).

Option (a) is no reason at all, since the ratio of two vectors is not defined by simple division. Option (b) is wrong because the magnitude of the whole force would include any tangential (shear) component, which does not contribute to pressure.

Question 8

A wooden block with a coin placed on its top floats in water as shown in Fig. 10.3. The distances $l$ and $h$ are shown in the figure. After some time the coin falls into the water. Then

Solution. Here $l$ is the depth of the block below the water surface and $h$ the depth of water in the vessel.

The block. While the coin rides on the block, the block must displace water weighing as much as block plus coin. Once the coin falls off, the block supports only its own weight, so it displaces less water and floats higher: $l$ decreases.

The water level. Let the coin have mass $m$ and density $\rho_c$. On the block, the coin’s weight is carried by buoyancy, so it displaces a volume $m/\rho_w$ of water. On the bottom of the vessel it displaces only its own volume, $m/\rho_c$. A coin is much denser than water, so $m/\rho_c < m/\rho_w$: the total volume of water displaced goes down and the level falls. So $h$ decreases.

Question 9

With increase in temperature, the viscosity of

Solution. The two kinds of fluid get their viscosity from different mechanisms. In a liquid, viscosity comes from the cohesive forces between closely packed molecules; heating gives the molecules more energy to break free of their neighbours, so layers slide over each other more easily and the viscosity falls (d). In a gas the molecules are far apart, and viscosity comes from molecules carrying momentum between layers as they move across; heating makes them move faster, so more momentum is transferred and the viscosity rises (c).

Question 10

Streamline flow is more likely for liquids with

Solution. Turbulence sets in when the inertia of the moving fluid, which tends to carry eddies along, wins over the viscous forces that damp them out. The inertia per unit volume goes as the density $\rho$, and the damping as the viscosity $\eta$; the ratio is the Reynolds number $\rho v d/\eta$, and the flow stays streamline while it is small. So a low density (c) and a high viscosity (b) both favour streamline flow. Honey poured from a spoon flows smoothly for this reason, while water at the same speed breaks up. (The current NCERT textbook no longer names the Reynolds number, but the comparison of inertia with viscous drag is all this question needs.)

Common mistakes

• Choosing a straight line in Question 1. Drag grows with speed, so the acceleration falls steadily; the graph must curve and flatten.
• Using the ratio of diameters in Question 4. Continuity is about area, so the speed ratio is the square of the diameter ratio, $9:4$, not $3:2$.
• Saying “net downward force” in Question 6. A molecule in a surface at rest is in equilibrium; the unbalanced pull is only the attractive part of the force.
• Thinking the water level rises in Question 8. A floating coin displaces its weight of water; a sunken coin displaces only its volume, which is smaller.
• Treating gases like liquids in Question 9. Heating lowers a liquid’s viscosity but raises a gas’s, because the mechanisms are different.

Practise next

• Water enters a horizontal pipe of diameter 4 cm at $0.5\ \text{m s}^{-1}$. The pipe narrows to a diameter of 2 cm. Find the speed in the narrow section.

• A block of wood of density $600\ \text{kg m}^{-3}$ floats in water. What fraction of its volume is above the surface?

• Exemplar Mechanical Properties of Fluids: Very Short, Short and Long Answer Questions — the same ideas applied to capillary rise, drops, the atmosphere and a hot-air balloon.
• NCERT textbook Chapter 9 — Mechanical Properties of Fluids for the theory of pressure, streamline flow, Bernoulli’s principle, viscosity and surface tension.
• Exemplar Mechanical Properties of Solids — the previous unit, on stress, strain and the elastic moduli.
• Exemplar Thermal Properties of Matter — the next unit, on expansion, calorimetry and heat transfer.