JEE Physics Mechanical Properties Of Fluids MCQs Set 11

Physics Objective Questions and Answers: Mechanical Properties Of Fluids

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Multiple Choice Questions

Question 1: A homogeneous solid cylinder of length L (L less than H/2) and cross-sectional area A/5 floats with its axis vertical at the interface of two liquids with length L/4 in the denser liquid. The upper liquid has density d and the lower 2d. The density D of the solid is:
(a) \( \tfrac54d \)
(b) \( \tfrac45d \)
(c) 4d
(d) \( d/5 \)
Show Answer & Explanation

Answer: (a) \( \tfrac54d \)

Explanation:
1. Weight = buoyant force: D L = (2d)(L/4) + d(3L/4)
2. D = 5d/4

Teacher's Note:
1. Apply the standard formula and check the units.

Question 2: A ball rises to the surface at a constant velocity in a liquid whose density is 4 times that of the material of the ball. The ratio of the force of friction acting on the rising ball to its weight is:
(a) 3 : 1
(b) 4 : 1
(c) 1 : 3
(d) 1 : 4
Show Answer & Explanation

Answer: (a) 3 : 1

Explanation:
1. Upthrust = 4 W, and at constant velocity upthrust = W + friction
2. Friction = 3W

Teacher's Note:
1. Apply the standard formula and check the units.

Question 3: If a ball of steel (density 7.8 g/cm3) attains a terminal velocity of 10 cm/s when falling in water (eta = 8.5e-4 Pa s), its terminal velocity in glycerine (density 1.2 g/cm3, eta = 13.2 Pa s) would be nearly:
(a) \( 1.6\times10^{-5} \) cm/s
(b) \( 3.98\times10^{-4} \) cm/s
(c) \( 6.25\times10^{-4} \) cm/s
(d) \( 1.5\times10^{-5} \) cm/s
Show Answer & Explanation

Answer: (c) \( 6.25\times10^{-4} \) cm/s

Explanation:
1. v is proportional to (rho - sigma)/eta
2. v = 10 x (6.6/13.2) x (8.5e-4/6.8) = 6.25e-4 cm/s

Teacher's Note:
1. Apply the standard formula and check the units.

Question 4: If more air is pushed into a soap bubble, the pressure inside it:
(a) decreases
(b) increases
(c) remains the same
(d) becomes zero
Show Answer & Explanation

Answer: (a) decreases

Explanation:
1. The bubble expands and its radius increases, so the excess pressure 4T/r decreases

Teacher's Note:
1. Apply the standard formula and check the units.

Question 5: The bulk modulus of a metal is \( 10^{10} \) N/m2 and its Poisson's ratio is 0.20. If the average distance between its molecules is 3 angstrom, the interatomic force constant is:
(a) 5.4 N/m
(b) 7.5 N/m
(c) 75 N/m
(d) 30 N/m
Show Answer & Explanation

Answer: (a) 5.4 N/m

Explanation:
1. Y = 3B(1 - 2 sigma) = 3 x 1e10 x 0.6 = 1.8e10 N/m2
2. k = Y r0 = 1.8e10 x 3e-10 = 5.4 N/m

Teacher's Note:
1. Apply the standard formula and check the units.

Question 6: There is no change in the volume of a wire due to a change in its length on stretching. The Poisson's ratio of the material is:
(a) +0.50
(b) -0.50
(c) 0.25
(d) -0.25
Show Answer & Explanation

Answer: (a) +0.50

Explanation:
1. For no volume change the lateral contraction is half the longitudinal strain, so sigma = 0.5

Teacher's Note:
1. Apply the standard formula and check the units.

Question 7: When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure equals that of a column of water of height H, the depth of the lake is:
(a) H
(b) 2H
(c) 7H
(d) 8H
Show Answer & Explanation

Answer: (c) 7H

Explanation:
1. Isothermal: (H + h) V1 = H (8 V1)
2. H + h = 8H, so h = 7H

Teacher's Note:
1. Apply the standard formula and check the units.

Question 8: A wooden cube just floats inside water when a 200 g mass is placed on it. When the mass is removed, the cube is 2 cm above the water level. The side of the cube is:
(a) 5 cm
(b) 10 cm
(c) 15 cm
(d) 20 cm
Show Answer & Explanation

Answer: (b) 10 cm

Explanation:
1. With side a (cm), the extra buoyant volume is a^2 x 2 cm3, which carries 200 g
2. 2a^2 = 200, so a = 10 cm

Teacher's Note:
1. Apply the standard formula and check the units.

Question 9: Water stands up to a height h behind the vertical wall of a dam. The net horizontal force pushing the dam down the stream, if the width of the dam is sigma, is:
(a) \( 2h\sigma\rho g \)
(b) \( h^2\sigma\rho g/2 \)
(c) \( h^2\sigma\rho g/4 \)
(d) \( h\sigma\rho g/4 \)
Show Answer & Explanation

Answer: (b) \( h^2\sigma\rho g/2 \)

Explanation:
1. Mean pressure rho g h/2 acts over area h sigma
2. Force = rho g h^2 sigma/2

Teacher's Note:
1. Apply the standard formula and check the units.

Question 10: A U-tube is partially filled with water. Oil which does not mix with water is next poured into one side until the water rises by 25 cm on the other side. If the density of the oil is 0.8 g/cc, the oil level will stand higher than the water level by:
(a) 6.25 cm
(b) 12.50 cm
(c) 18.75 cm
(d) 25.00 cm
Show Answer & Explanation

Answer: (b) 12.50 cm

Explanation:
1. The water levels differ by 50 cm, so the oil column is 50/0.8 = 62.5 cm
2. The oil surface is 62.5 - 50 = 12.5 cm above the water surface on the other side

Teacher's Note:
1. Apply the standard formula and check the units.

Question 11: A hole is in the bottom of a tank of water. If the total pressure at the bottom is 3 atm (1 atm = 100000 N/m2), the velocity of water flowing from the hole is:
(a) \( \sqrt{400} \) m/s
(b) \( \sqrt{600} \) m/s
(c) \( \sqrt{60} \) m/s
(d) none of these
Show Answer & Explanation

Answer: (a) \( \sqrt{400} \) m/s

Explanation:
1. The gauge pressure is 2 atm = 2e5 Pa
2. v = sqrt(2 x 2e5/1000) = sqrt(400) m/s

Teacher's Note:
1. Apply the standard formula and check the units.

Question 12: Water moves with a speed of 5.0 m/s through a pipe of cross-sectional area 4.0 cm2. The water gradually descends 10 m as the pipe increases in area to 8.0 cm2. If the pressure at the upper level is \( 1.5\times10^5 \) Pa, the pressure at the lower level is (g = 10 m/s2):
(a) \( 2.8\times10^5 \) Pa
(b) \( 2.6\times10^5 \) Pa
(c) \( 2.4\times10^5 \) Pa
(d) \( 2.1\times10^5 \) Pa
Show Answer & Explanation

Answer: (b) \( 2.6\times10^5 \) Pa

Explanation:
1. Continuity: v2 = 5 x 4/8 = 2.5 m/s
2. P2 = P1 + rho g h + (1/2) rho (v1^2 - v2^2) = 1.5e5 + 1e5 + 500 x 18.75 = 2.59e5 Pa

Teacher's Note:
1. Apply the standard formula and check the units.

Question 13: The terminal speed attained by an aluminium sphere of radius 1 mm falling through water at 20 C is close to (laminar flow assumed, specific gravity of Al = 2.7, eta of water = 8e-4 Pl):
(a) 9.2 m/s
(b) 6.9 m/s
(c) 4.6 m/s
(d) 2.3 m/s
Show Answer & Explanation

Answer: (c) 4.6 m/s

Explanation:
1. v = 2 r^2 (rho - sigma) g/(9 eta) = 2 x 1e-6 x 1700 x 9.8/(9 x 8e-4) = 4.6 m/s

Teacher's Note:
1. Apply the standard formula and check the units.

Question 14: If the difference between the pressure inside and outside a soap bubble is 6 mm of water and its radius is 8 mm, the surface tension in dynes per cm is:
(a) 117.6
(b) 256
(c) 378
(d) 450
Show Answer & Explanation

Answer: (a) 117.6

Explanation:
1. Pressure difference = 0.6 cm x 1 x 980 = 588 dyne/cm2
2. For a bubble T = delta P x r/4 = 588 x 0.8/4 = 117.6 dyne/cm

Teacher's Note:
1. Apply the standard formula and check the units.

Question 15: An air bubble lying just below the surface of water has radius 1 mm. The surface tension of water is 70e-3 N/m and the atmospheric pressure is 1.013e5 N/m2. The pressure inside the bubble is:
(a) \( 1.0270\times10^5 \) Pa
(b) \( 1.0160\times10^5 \) Pa
(c) \( 1.0144\times10^5 \) Pa
(d) \( 1.0131\times10^5 \) Pa
Show Answer & Explanation

Answer: (c) \( 1.0144\times10^5 \) Pa

Explanation:
1. A bubble in a liquid has one surface: delta P = 2T/r = 2 x 0.07/1e-3 = 140 Pa
2. P = 1.013e5 + 140 = 1.0144e5 Pa

Teacher's Note:
1. Apply the standard formula and check the units.

Question 16: The diameters of the two limbs of a U-tube are 2 mm and 5 mm and the surface tension of water is 70 dyne/cm. If the density of water is 1000 kg/m3 and g = 10 m/s2, the water level difference in the two tubes will be:
(a) 8.4 m
(b) 8.4 cm
(c) 84 cm
(d) 0.84 cm
Show Answer & Explanation

Answer: (d) 0.84 cm

Explanation:
1. Delta h = (2T/rho g)(1/r1 - 1/r2) = (0.14/1e4)(1000 - 400) = 8.4e-3 m = 0.84 cm

Teacher's Note:
1. Apply the standard formula and check the units.

Question 17: A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of water in the capillary tube is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is:
(a) 2.5 g
(b) 5.0 g
(c) 10 g
(d) 20 g
Show Answer & Explanation

Answer: (c) 10 g

Explanation:
1. Mass is proportional to r, so doubling the radius doubles the mass to 10 g

Teacher's Note:
1. Apply the standard formula and check the units.

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Mechanical Properties Of Fluids Objective Questions & Solutions for JEE Physics

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