Grade 11 : Physics - Fluids (Set 3)

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Grade 11 : Physics - Fluids (Set 3)— Questions & Detailed Solutions

Cross-section schematic: A hydraulic lift consists of two vertical connected cylinders containing an incompressible fluid sealed by pistons of radii $r_1 = 2cm$ and $r_2 = 10cm$.
In a hydraulic lift, a force $F_1 = 50\text{ N}$ is applied to the smaller piston of radius $r_1 = 2cm$. What is the magnitude of the force $F_2$ exerted by the fluid on the larger piston of radius $r_2 = 10cm$?

(A)

250 N

(B)

500 N

(C)

1250 N

(D)

2500 N

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: According to Pascal's Law, pressure is transmitted equally throughout an enclosed fluid:
$$\frac{F_1}{A_1} = \frac{F_2}{A_2} \implies F_2 = F_1 \left(\frac{r_2}{r_1}\right)^2$$
Substitute given values:
$$F_2 = 50 \times \left(\frac{10}{2}\right)^2 = 50 \times 25 = 1250\text{ N}$$

Calculate the gauge pressure at a depth of 20 m below the surface of a fresh water lake ($\rho = 1000\text{ kg/m}^3$). Take acceleration due to gravity $g = 9.8m/s^2$.

(A)

98 kPa

(B)

196 kPa

(C)

294 kPa

(D)

392 kPa

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Gauge pressure at depth $h$ is given by $P_g = \rho g h$.
$$P_g = 1000\text{ kg/m}^3 \times 9.8\text{ m/s}^2 \times 20\text{ m} = 196,000\text{ Pa} = 196\text{ kPa}$$

A solid aluminum block of volume $V = 0.002m^3$ and density $\rho_b = 2700\text{ kg/m}^3$ is completely submerged in water (density $\rho_w = 1000\text{ kg/m}^3$). Taking $g = 10m/s^2$, what is the apparent weight of the submerged block?

(A)

20 N

(B)

34 N

(C)

54 N

(D)

74 N

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Actual Weight $W = \rho_b V g = 2700 \times 0.002 \times 10 = 54\text{ N}$.
Buoyant force $F_b = \rho_w V g = 1000 \times 0.002 \times 10 = 20\text{ N}$.
Apparent weight $W_{app} = W - F_b = 54 - 20 = 34\text{ N}$.

A wooden block floats in a liquid of density $\rho_l = 1200\text{ kg/m}^3$ with 75% of its total volume submerged below the surface. What is the density of the wooden block?

(A)

$600\text{ kg/m}^3$

(B)

$800\text{ kg/m}^3$

(C)

$900\text{ kg/m}^3$

(D)

$1000\text{ kg/m}^3$

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: For flotation, Weight of block = Buoyant force:
$$\rho_{wood} V_{total} g = \rho_l V_{submerged} g \implies \rho_{wood} = \rho_l \left(\frac{V_{submerged}}{V_{total}}\right)$$
$$\rho_{wood} = 1200 \times 0.75 = 900\text{ kg/m}^3$$

Water flows through a horizontal pipe of non-uniform diameter. At section 1, the diameter is 6 cm and fluid velocity is 2 m/s. If section 2 narrows to a diameter of 3 cm, what is the flow speed at section 2?

(A)

4 m/s

(B)

6 m/s

(C)

8 m/s

(D)

12 m/s

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: By the Equation of Continuity for incompressible fluids:
$$A_1 v_1 = A_2 v_2 \implies d_1^2 v_1 = d_2^2 v_2$$
$$(6)^2 \times 2 = (3)^2 \times v_2 \implies 36 \times 2 = 9 v_2 \implies v_2 = 8\text{ m/s}$$

An open water tank has a small orifice drilled 5 m below the water surface level. Assuming $g = 9.8m/s^2$, what is the speed of efflux of water leaving the orifice?

(A)

7.0 m/s

(B)

9.9 m/s

(C)

14.0 m/s

(D)

19.6 m/s

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: According to Torricelli's Law, efflux velocity is:
$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} = \sqrt{98} \approx 9.9\text{ m/s}$$

A soap bubble in air has a radius of 2 cm. If the surface tension of the soap solution is $T = 0.03\text{ N/m}$, what is the excess pressure inside the bubble relative to ambient atmospheric pressure?

(A)

1.5 Pa

(B)

3.0 Pa

(C)

6.0 Pa

(D)

12.0 Pa

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: A soap bubble has two liquid-air surfaces, so excess pressure is:
$$\Delta P = \frac{4T}{R} = \frac{4 \times 0.03}{0.02\text{ m}} = 6\text{ Pa}$$

When capillary tube A of radius $r_A = 0.4\text{ mm}$ is dipped vertically into water, the liquid rises to a height of 3 cm. What height will water rise in capillary tube B of radius $r_B = 0.2\text{ mm}$ placed in the same liquid?

(A)

1.5 cm

(B)

3.0 cm

(C)

6.0 cm

(D)

12.0 cm

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: According to Jurin's Law, height of capillary rise is inversely proportional to radius ($h \cdot r = \text{constant}$):
$$h_A r_A = h_B r_B \implies 3\text{ cm} \times 0.4\text{ mm} = h_B \times 0.2\text{ mm} \implies h_B = 6\text{ cm}$$

Two spherical raindrops of radii in the ratio $1:2$ fall vertically through air under viscous drag. Assuming both drops reach terminal velocity, what is the ratio of their terminal velocities ($v_1 : v_2$)?

(A)

$1 : 2$

(B)

$1 : 4$

(C)

$1 : 8$

(D)

$1 : 16$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Terminal velocity of a sphere falling through a viscous fluid is given by Stokes' formula: $v_t \propto r^2$.
$$\frac{v_1}{v_2} = \left(\frac{r_1}{r_2}\right)^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}$$

Q10

Venturimeter setup: Water flows along a horizontal streamline pipe from wide cross-section 1 to narrow throat cross-section 2.
Water (density $\rho = 1000\text{ kg/m}^3$) flows horizontally through a pipe. At section 1, flow speed is 1 m/s and static pressure is 200 kPa. At a narrower section 2, speed increases to 5 m/s. Neglecting friction, what is the static pressure at section 2?

(A)

176 kPa

(B)

188 kPa

(C)

192 kPa

(D)

212 kPa

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Apply Bernoulli's equation along horizontal streamline ($h_1 = h_2$):
$$P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$$
$$200,000 + \frac{1}{2}(1000)(1)^2 = P_2 + \frac{1}{2}(1000)(5)^2$$
$$200,500 = P_2 + 12,500 \implies P_2 = 188,000\text{ Pa} = 188\text{ kPa}$$

Q11

Eight identical small spherical water droplets, each of radius $r$, coalesce to form a single larger spherical drop of radius $R$. What is the relationship between $R$ and $r$?

(A)

$R = 1.5 r$

(B)

$R = 2 r$

(C)

$R = 4 r$

(D)

$R = 8 r$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Total volume remains constant during coalescence:
$$\frac{4}{3}\pi R^3 = 8 \times \left(\frac{4}{3}\pi r^3\right) \implies R^3 = 8r^3 \implies R = 2r$$

Q12

How much work must be done against surface tension to blow a soap bubble of radius $R = 5cm$ if the surface tension of liquid is $T = 0.04\text{ N/m}$?

(A)

$2\pi \times 10^{-4}\text{ J}$

(B)

$4\pi \times 10^{-4}\text{ J}$

(C)

$8\pi \times 10^{-4}\text{ J}$

(D)

$16\pi \times 10^{-4}\text{ J}$

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: A soap bubble has 2 free surfaces, so total surface area created is $\Delta A = 2 \times 4\pi R^2 = 8\pi R^2$.
Work done $W = T \Delta A = 0.04 \times 8\pi \times (0.05)^2 = 0.04 \times 8\pi \times 0.0025 = 8\pi \times 10^{-4}\text{ J}$.

Q13

A fluid of density $\rho = 1000\text{ kg/m}^3$ and dynamic viscosity $\eta = 10^{-3}\text{ Pa}\cdot\text{s}$ flows through a tube of internal diameter $d = 0.02m$ at an average speed of $v = 0.1m/s$. Calculate the Reynolds number ($R_e$) of the flow.

(A)

200

(B)

1000

(C)

2000

(D)

4000

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Reynolds number formula:
$$R_e = \frac{\rho v d}{\eta} = \frac{1000 \times 0.1 \times 0.02}{10^{-3}} = \frac{2}{10^{-3}} = 2000$$

Q14

A small spherical ball of radius $r = 1\text{ mm}$ falls through castor oil ($\eta = 0.5\text{ Pa}\cdot\text{s}$) with a uniform velocity $v = 0.2m/s$. Calculate the retarding viscous force acting on the ball.

(A)

$3\pi \times 10^{-4}\text{ N}$

(B)

$6\pi \times 10^{-4}\text{ N}$

(C)

$1.2\pi \times 10^{-3}\text{ N}$

(D)

$3\pi \times 10^{-3}\text{ N}$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: By Stokes' Law, viscous drag force is:
$$F = 6\pi \eta r v = 6\pi \times 0.5 \times 10^{-3}\text{ m} \times 0.2\text{ m/s} = 6\pi \times 10^{-4}\text{ N}$$

Q15

Liquid Column Height ($h$) Density ($\rho$)
Water 12 cm $1000\text{ kg/m}^3$
Oil 15 cm Unknown ($\rho_o$)
An open U-tube manometer contains water and an immiscible oil in hydrostatic equilibrium. A water column of height 12 cm balances an oil column of height 15 cm. What is the density of the oil?

Liquid Column	Height ($h$)	Density ($\rho$)
Water	12 cm	$1000\text{ kg/m}^3$
Oil	15 cm	Unknown ($\rho_o$)

(A)

$600\text{ kg/m}^3$

(B)

$750\text{ kg/m}^3$

(C)

$800\text{ kg/m}^3$

(D)

$900\text{ kg/m}^3$

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: At the interface interface baseline, pressures are equal:
$$\rho_o g h_o = \rho_w g h_w \implies \rho_o = \rho_w \left(\frac{h_w}{h_o}\right)$$
$$\rho_o = 1000 \times \left(\frac{12}{15}\right) = 800\text{ kg/m}^3$$

Q16

A tall cylinder of total height $H = 16m$ is completely filled with water. A small hole is drilled on its vertical side wall. At what depth $h$ below the top surface should the hole be drilled to achieve maximum horizontal range of efflux on the ground level?

(A)

4 m

(B)

6 m

(C)

8 m

(D)

12 m

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Horizontal range $R = 2\sqrt{h(H-h)}$. Range $R$ is maximum when $h = \frac{H}{2}$.
$$h = \frac{16\text{ m}}{2} = 8\text{ m}$$

Q17

Statement I: If the angle of contact $\theta < 90^\circ$, the liquid wets the solid container surface and rises in a capillary tube.
Statement II: For mercury in contact with glass, the contact angle is obtuse ($\theta > 90^\circ$), resulting in capillary depression.
Which of the following evaluations regarding Statements I and II is correct?

(A)

Both Statement I and Statement II are true.

(B)

Both Statement I and Statement II are false.

(C)

Statement I is true, but Statement II is false.

(D)

Statement I is false, but Statement II is true.

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: When $\theta < 90^\circ$ (adhesive force > cohesive force), liquid wets the wall and ascends capillary. For mercury-glass, cohesive forces dominate so $\theta \approx 138^\circ > 90^\circ$, causing meniscus depression. Both statements are scientifically true.

Q18

Standard atmospheric pressure supports a 76 cm column of mercury (density $\rho_{Hg} = 13,600\text{ kg/m}^3$). If a simple barometer uses pure water (density $\rho_w = 1000\text{ kg/m}^3$) instead of mercury, what height of water column corresponds to 1 atm pressure ($1.013 \times 10^5\text{ Pa}$)? ($g = 9.8m/s^2$)

(A)

0.76 m

(B)

5.20 m

(C)

10.33 m

(D)

13.60 m

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Hydrostatic pressure relation $P = \rho_w g h_w$.
$$h_w = \frac{P}{\rho_w g} = \frac{1.013 \times 10^5}{1000 \times 9.8} \approx 10.33\text{ m}$$

Q19

An aeroplane wing (aerofoil) is designed such that air streams past the upper wing surface at $v_1 = 80m/s$ and lower wing surface at $v_2 = 60m/s$. Air density $\rho = 1.2\text{ kg/m}^3$, and total wing surface area is $A = 20m^2$.
Using Bernoulli's principle, calculate the total upward dynamic lift force acting on the aeroplane wings.

(A)

16.8 kN

(B)

33.6 kN

(C)

50.4 kN

(D)

67.2 kN

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Pressure difference between bottom and top surface:
$$\Delta P = \frac{1}{2}\rho (v_1^2 - v_2^2) = \frac{1}{2}(1.2)(80^2 - 60^2) = 0.6 \times (6400 - 3600) = 1680\text{ Pa}$$
Lift force $F = \Delta P \times A = 1680 \times 20 = 33,600\text{ N} = 33.6\text{ kN}$.

Q20

A horizontal flat plate of area $A = 0.01m^2$ rests on a layer of oil of thickness $d = 2\text{ mm} = 0.002m$ over a fixed horizontal table. The coefficient of viscosity of the oil is $\eta = 0.8\text{ Pa}\cdot\text{s}$. What horizontal force is required to move the plate at a constant velocity $v = 0.5m/s$?

(A)

0.5 N

(B)

1.0 N

(C)

2.0 N

(D)

4.0 N

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: According to Newton's law of viscosity:
$$F = \eta A \frac{v}{d} = 0.8 \times 0.01 \times \left(\frac{0.5}{0.002}\right) = 0.008 \times 250 = 2.0\text{ N}$$

Grade 11 : Physics - Fluids (Set 3)

Grade 11 : Physics - Fluids (Set 3)— Questions & Detailed Solutions

Calculate the gauge pressure at a depth of 20 m below the surface of a fresh water lake ($\rho = 1000\text{ kg/m}^3$). Take acceleration due to gravity $g = 9.8m/s^2$.

A solid aluminum block of volume $V = 0.002m^3$ and density $\rho_b = 2700\text{ kg/m}^3$ is completely submerged in water (density $\rho_w = 1000\text{ kg/m}^3$). Taking $g = 10m/s^2$, what is the apparent weight of the submerged block?

A wooden block floats in a liquid of density $\rho_l = 1200\text{ kg/m}^3$ with 75% of its total volume submerged below the surface. What is the density of the wooden block?

Water flows through a horizontal pipe of non-uniform diameter. At section 1, the diameter is 6 cm and fluid velocity is 2 m/s. If section 2 narrows to a diameter of 3 cm, what is the flow speed at section 2?

An open water tank has a small orifice drilled 5 m below the water surface level. Assuming $g = 9.8m/s^2$, what is the speed of efflux of water leaving the orifice?

A soap bubble in air has a radius of 2 cm. If the surface tension of the soap solution is $T = 0.03\text{ N/m}$, what is the excess pressure inside the bubble relative to ambient atmospheric pressure?

When capillary tube A of radius $r_A = 0.4\text{ mm}$ is dipped vertically into water, the liquid rises to a height of 3 cm. What height will water rise in capillary tube B of radius $r_B = 0.2\text{ mm}$ placed in the same liquid?

Two spherical raindrops of radii in the ratio $1:2$ fall vertically through air under viscous drag. Assuming both drops reach terminal velocity, what is the ratio of their terminal velocities ($v_1 : v_2$)?

Eight identical small spherical water droplets, each of radius $r$, coalesce to form a single larger spherical drop of radius $R$. What is the relationship between $R$ and $r$?

How much work must be done against surface tension to blow a soap bubble of radius $R = 5cm$ if the surface tension of liquid is $T = 0.04\text{ N/m}$?

A fluid of density $\rho = 1000\text{ kg/m}^3$ and dynamic viscosity $\eta = 10^{-3}\text{ Pa}\cdot\text{s}$ flows through a tube of internal diameter $d = 0.02m$ at an average speed of $v = 0.1m/s$. Calculate the Reynolds number ($R_e$) of the flow.

A small spherical ball of radius $r = 1\text{ mm}$ falls through castor oil ($\eta = 0.5\text{ Pa}\cdot\text{s}$) with a uniform velocity $v = 0.2m/s$. Calculate the retarding viscous force acting on the ball.

Liquid Column Height ($h$) Density ($\rho$)
Water 12 cm $1000\text{ kg/m}^3$
Oil 15 cm Unknown ($\rho_o$)
An open U-tube manometer contains water and an immiscible oil in hydrostatic equilibrium. A water column of height 12 cm balances an oil column of height 15 cm. What is the density of the oil?

A tall cylinder of total height $H = 16m$ is completely filled with water. A small hole is drilled on its vertical side wall. At what depth $h$ below the top surface should the hole be drilled to achieve maximum horizontal range of efflux on the ground level?

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Grade 11 : Physics - Fluids (Set 3)

Grade 11 : Physics - Fluids (Set 3)— Questions & Detailed Solutions

Calculate the gauge pressure at a depth of 20 m below the surface of a fresh water lake ($\rho = 1000\text{ kg/m}^3$). Take acceleration due to gravity $g = 9.8m/s^2$.

A solid aluminum block of volume $V = 0.002m^3$ and density $\rho_b = 2700\text{ kg/m}^3$ is completely submerged in water (density $\rho_w = 1000\text{ kg/m}^3$). Taking $g = 10m/s^2$, what is the apparent weight of the submerged block?

A wooden block floats in a liquid of density $\rho_l = 1200\text{ kg/m}^3$ with 75% of its total volume submerged below the surface. What is the density of the wooden block?

Water flows through a horizontal pipe of non-uniform diameter. At section 1, the diameter is 6 cm and fluid velocity is 2 m/s. If section 2 narrows to a diameter of 3 cm, what is the flow speed at section 2?

An open water tank has a small orifice drilled 5 m below the water surface level. Assuming $g = 9.8m/s^2$, what is the speed of efflux of water leaving the orifice?

A soap bubble in air has a radius of 2 cm. If the surface tension of the soap solution is $T = 0.03\text{ N/m}$, what is the excess pressure inside the bubble relative to ambient atmospheric pressure?

When capillary tube A of radius $r_A = 0.4\text{ mm}$ is dipped vertically into water, the liquid rises to a height of 3 cm. What height will water rise in capillary tube B of radius $r_B = 0.2\text{ mm}$ placed in the same liquid?

Two spherical raindrops of radii in the ratio $1:2$ fall vertically through air under viscous drag. Assuming both drops reach terminal velocity, what is the ratio of their terminal velocities ($v_1 : v_2$)?

Eight identical small spherical water droplets, each of radius $r$, coalesce to form a single larger spherical drop of radius $R$. What is the relationship between $R$ and $r$?

How much work must be done against surface tension to blow a soap bubble of radius $R = 5cm$ if the surface tension of liquid is $T = 0.04\text{ N/m}$?

A fluid of density $\rho = 1000\text{ kg/m}^3$ and dynamic viscosity $\eta = 10^{-3}\text{ Pa}\cdot\text{s}$ flows through a tube of internal diameter $d = 0.02m$ at an average speed of $v = 0.1m/s$. Calculate the Reynolds number ($R_e$) of the flow.

A small spherical ball of radius $r = 1\text{ mm}$ falls through castor oil ($\eta = 0.5\text{ Pa}\cdot\text{s}$) with a uniform velocity $v = 0.2m/s$. Calculate the retarding viscous force acting on the ball.

Liquid ColumnHeight ($h$)Density ($\rho$)Water12 cm$1000\text{ kg/m}^3$Oil15 cmUnknown ($\rho_o$)An open U-tube manometer contains water and an immiscible oil in hydrostatic equilibrium. A water column of height 12 cm balances an oil column of height 15 cm. What is the density of the oil?

A tall cylinder of total height $H = 16m$ is completely filled with water. A small hole is drilled on its vertical side wall. At what depth $h$ below the top surface should the hole be drilled to achieve maximum horizontal range of efflux on the ground level?

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Liquid Column Height ($h$) Density ($\rho$)
Water 12 cm $1000\text{ kg/m}^3$
Oil 15 cm Unknown ($\rho_o$)
An open U-tube manometer contains water and an immiscible oil in hydrostatic equilibrium. A water column of height 12 cm balances an oil column of height 15 cm. What is the density of the oil?