Mechanical Properties of Fluids Chapter-Wise Test 8

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A plate of area \( 0.06 \, \text{m}^2 \) moves at \( 0.9 \, \text{m/s} \) over a \( 0.5 \, \text{mm} \) thick honey film (\( \eta = 0.2 \, \text{Pa s} \)). What force is required?

Viscous force: \( F = \eta \frac{v A}{l} \).

\( \eta = 0.2 \, \text{Pa s} \), \( v = 0.9 \, \text{m/s} \), \( A = 0.06 \, \text{m}^2 \), \( l = 0.5 \times 10^{-3} \, \text{m} \).

\( F = 0.2 \times \frac{0.9 \times 0.06}{0.5 \times 10^{-3}} = 0.2 \times 108 = 21.6 \, \text{N} \).

18 N
20 N
22 N
24 N
3

What causes the pressure inside a soap bubble to be higher than outside?

Surface tension at the bubble’s two interfaces (inner and outer) creates an excess pressure (\( \Delta P = 4S/r \)) to balance the tendency of the curved surface to contract, increasing internal pressure above atmospheric pressure.

Viscosity of the soap solution
Surface tension at the interfaces
Atmospheric pressure decrease
Density of the soap film
2

A hydraulic lift uses a small piston of area \( 0.02 \, \text{m}^2 \) to exert a force of \( 200 \, \text{N} \) to lift a load with a large piston of area \( 0.1 \, \text{m}^2 \). What is the mass of the load? (Take \( g = 10 \, \text{m/s}^2 \))

Pascal’s law: \( P = \frac{F_1}{A_1} = \frac{F_2}{A_2} \).

\( F_2 = F_1 \times \frac{A_2}{A_1} \).

\( F_1 = 200 \, \text{N} \), \( A_1 = 0.02 \, \text{m}^2 \), \( A_2 = 0.1 \, \text{m}^2 \).

\( F_2 = 200 \times \frac{0.1}{0.02} = 200 \times 5 = 1000 \, \text{N} \).

\( m = \frac{F_2}{g} = \frac{1000}{10} = 100 \, \text{kg} \).

80 kg
90 kg
100 kg
110 kg
3

A capillary tube of radius \( 0.4 \, \text{mm} \) is dipped in water (\( S = 0.0727 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( \cos \theta = 1 \)). What is the capillary rise? (Take \( g = 9.8 \, \text{m/s}^2 \))

\( h = \frac{2 S \cos \theta}{\rho g a} \).

\( S = 0.0727 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( g = 9.8 \, \text{m/s}^2 \), \( a = 0.4 \times 10^{-3} \, \text{m} \).

\( h = \frac{2 \times 0.0727 \times 1}{1000 \times 9.8 \times 0.4 \times 10^{-3}} = 0.03714 \, \text{m} = 3.71 \, \text{cm} \).

3.0 cm
3.7 cm
4.2 cm
4.8 cm
2

A bubble of radius \( 6.5 \, \text{mm} \) is blown at \( 55 \, \text{cm} \) depth in water (\( \rho = 1000 \, \text{kg/m}^3 \), \( S = 0.0727 \, \text{N/m} \)). What is the total pressure inside? (Take \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 9.8 \, \text{m/s}^2 \))

\( P_i = P_a + \rho g h + \frac{2 S}{r} \).

\( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( \rho g h = 1000 \times 9.8 \times 0.55 = 5390 \, \text{Pa} \).

\( \frac{2 S}{r} = \frac{2 \times 0.0727}{6.5 \times 10^{-3}} = 22.34 \, \text{Pa} \).

\( P_i = 1.01 \times 10^5 + 5390 + 22.34 = 1.06392 \times 10^5 \, \text{Pa} \).

1.05 × 10⁵ Pa
1.06 × 10⁵ Pa
1.07 × 10⁵ Pa
1.08 × 10⁵ Pa
2

A soap film supports \( 3.0 \times 10^{-2} \, \text{N} \) over a \( 50 \, \text{cm} \) slider. What is the surface tension?

\( S = \frac{F}{2 l} \).

\( F = 3.0 \times 10^{-2} \, \text{N} \), \( l = 0.5 \, \text{m} \).

\( S = \frac{3.0 \times 10^{-2}}{2 \times 0.5} = 0.03 \, \text{N/m} \).

0.025 N/m
0.030 N/m
0.035 N/m
0.040 N/m
2

A car lift uses a small piston of radius \( 4 \, \text{cm} \) to lift a \( 1200 \, \text{kg} \) car on a piston of radius \( 12 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 10 \, \text{m/s}^2 \))

\( F_1 = \frac{A_1}{A_2} F_2 \), \( F_2 = mg = 1200 \times 10 = 12000 \, \text{N} \).

\( A_1 = \pi (0.04)^2 \), \( A_2 = \pi (0.12)^2 \).

\( \frac{A_1}{A_2} = \frac{(0.04)^2}{(0.12)^2} = \frac{0.0016}{0.0144} = \frac{1}{9} \).

\( F_1 = \frac{12000}{9} = 1333.33 \, \text{N} \approx 1333 \, \text{N} \).

1000 N
1333 N
1500 N
2000 N
2

A spray tube (\( 6 \, \text{cm}^2 \)) has 30 holes of diameter \( 1.2 \, \text{mm} \). If the flow speed is \( 1.8 \, \text{m/min} \), what is the ejection speed?

\( A_1 v_1 = A_2 v_2 \), \( v_1 = 1.8 \, \text{m/min} = 0.03 \, \text{m/s} \), \( A_1 = 6 \times 10^{-4} \, \text{m}^2 \).

Hole area: \( A_h = \pi (0.6 \times 10^{-3})^2 \), total \( A_2 = 30 \times \pi \times 3.6 \times 10^{-7} \approx 3.39 \times 10^{-5} \, \text{m}^2 \).

\( v_2 = \frac{6 \times 10^{-4} \times 0.03}{3.39 \times 10^{-5}} \approx 0.531 \, \text{m/s} \).

0.3 m/s
0.53 m/s
0.8 m/s
1.0 m/s
2

What is the gauge pressure at a depth of \( 2.9 \, \text{m} \) in water (\( \rho = 1000 \, \text{kg/m}^3 \))? (Take \( g = 10 \, \text{m/s}^2 \))

Gauge pressure: \( P_g = \rho g h \).

\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \), \( h = 2.9 \, \text{m} \).

\( P_g = 1000 \times 10 \times 2.9 = 29000 \, \text{Pa} = 2.9 \times 10^4 \, \text{Pa} \).

2.7 × 10⁴ Pa
2.8 × 10⁴ Pa
2.9 × 10⁴ Pa
3.0 × 10⁴ Pa
3

Water flows at \( 1.8 \, \text{m/s} \) at \( 2.8 \, \text{m} \) height with pressure \( 1.75 \times 10^5 \, \text{Pa} \). What is the pressure at \( 1.2 \, \text{m} \) height with speed \( 2.6 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \))

Bernoulli’s: \( P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2 \).

Left: \( 1.75 \times 10^5 + \frac{1}{2} \times 1000 \times 3.24 + 1000 \times 10 \times 2.8 = 1.75 \times 10^5 + 1620 + 28000 = 2.0462 \times 10^5 \).

Right: \( P_2 + \frac{1}{2} \times 1000 \times 6.76 + 1000 \times 10 \times 1.2 = P_2 + 3380 + 12000 = P_2 + 15380 \).

\( 2.0462 \times 10^5 = P_2 + 15380 \), \( P_2 = 1.8922 \times 10^5 \, \text{Pa} \).

1.85 × 10⁵ Pa
1.89 × 10⁵ Pa
1.95 × 10⁵ Pa
2.00 × 10⁵ Pa
2

A \( 65 \, \text{kg} \) person stands on two bones, each with area \( 20 \, \text{cm}^2 \). What is the average pressure on the bones? (Take \( g = 10 \, \text{m/s}^2 \))

\( P_{av} = \frac{F}{A} \), \( F = mg = 65 \times 10 = 650 \, \text{N} \).

Total area \( A = 2 \times 20 \times 10^{-4} = 4.0 \times 10^{-3} \, \text{m}^2 \).

\( P_{av} = \frac{650}{4.0 \times 10^{-3}} = 1.625 \times 10^5 \, \text{Pa} \).

1.5 × 10⁵ Pa
1.6 × 10⁵ Pa
1.625 × 10⁵ Pa
1.7 × 10⁵ Pa
3

A spray tube (\( 5 \, \text{cm}^2 \)) has 25 holes of diameter \( 1.0 \, \text{mm} \). If the flow speed is \( 2.4 \, \text{m/min} \), what is the ejection speed?

\( A_1 v_1 = A_2 v_2 \), \( v_1 = 2.4 \, \text{m/min} = 0.04 \, \text{m/s} \), \( A_1 = 5 \times 10^{-4} \, \text{m}^2 \).

Hole area: \( A_h = \pi (0.5 \times 10^{-3})^2 \), total \( A_2 = 25 \times \pi \times 2.5 \times 10^{-7} \approx 1.963 \times 10^{-5} \, \text{m}^2 \).

\( v_2 = \frac{5 \times 10^{-4} \times 0.04}{1.963 \times 10^{-5}} \approx 1.02 \, \text{m/s} \).

0.8 m/s
1.02 m/s
1.2 m/s
1.5 m/s
2

A plate of area \( 0.09 \, \text{m}^2 \) moves at \( 0.5 \, \text{m/s} \) over a \( 1.0 \, \text{mm} \) thick water film (\( \eta = 1.0 \times 10^{-3} \, \text{Pa s} \)). What force is required?

Viscous force: \( F = \eta \frac{v A}{l} \).

\( \eta = 1.0 \times 10^{-3} \, \text{Pa s} \), \( v = 0.5 \, \text{m/s} \), \( A = 0.09 \, \text{m}^2 \), \( l = 1.0 \times 10^{-3} \, \text{m} \).

\( F = 1.0 \times 10^{-3} \times \frac{0.5 \times 0.09}{1.0 \times 10^{-3}} = 1.0 \times 10^{-3} \times 45 = 0.045 \, \text{N} \).

0.04 N
0.045 N
0.05 N
0.06 N
2

A capillary tube of radius \( 0.15 \, \text{mm} \) is dipped in water (\( S = 0.0727 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( \cos \theta = 1 \)). What is the capillary rise? (Take \( g = 9.8 \, \text{m/s}^2 \))

\( h = \frac{2 S \cos \theta}{\rho g a} \).

\( S = 0.0727 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( g = 9.8 \, \text{m/s}^2 \), \( a = 0.15 \times 10^{-3} \, \text{m} \).

\( h = \frac{2 \times 0.0727 \times 1}{1000 \times 9.8 \times 0.15 \times 10^{-3}} = 0.0989 \, \text{m} = 9.89 \, \text{cm} \).

7.5 cm
9.9 cm
12.5 cm
15.0 cm
2

A pipe’s cross-sectional area decreases from \( 0.09 \, \text{m}^2 \) to \( 0.03 \, \text{m}^2 \). If water flows at \( 1.5 \, \text{m/s} \) in the larger section, what is the speed in the smaller section?

Continuity equation: \( A_1 v_1 = A_2 v_2 \).

\( A_1 = 0.09 \, \text{m}^2 \), \( v_1 = 1.5 \, \text{m/s} \), \( A_2 = 0.03 \, \text{m}^2 \).

\( v_2 = \frac{A_1 v_1}{A_2} = \frac{0.09 \times 1.5}{0.03} = 4.5 \, \text{m/s} \).

3.0 m/s
4.0 m/s
4.5 m/s
5.0 m/s
3

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