JEE Physics Mechanical Properties Of Fluids MCQs Set 15

Answer: (b) surface energy is decreased

Explanation:
1. The area of the large drop is less than the total area of the two droplets.
2. So surface energy decreases and the difference is released as heat.

Teacher's Note:
1. Merging reduces total surface area.
2. The energy released slightly warms the liquid.

Answer: (d) 2 × 10⁻⁴ J

Explanation:
1. A thin film has two free surfaces.
2. Surface energy = 2 T A = 2 × 50 × 0.02 × 10⁻⁴ = 2 × 10⁻⁴ J.

Teacher's Note:
1. Remember to include both surfaces of the film.
2. Convert cm² to m² using 10⁻⁴.

Answer: (a) AT

Explanation:
1. Surface energy = T × area.
2. The increase is T × A.

Teacher's Note:
1. Surface tension equals energy per unit area.
2. Units of T are J/m².

Answer: (c) 2 : 1

Explanation:
1. The large drop has radius 2R.
2. Before: 8 × 4π R² T = 32 π R² T. After: 4π (2R)² T = 16 π R² T. The ratio is 2 : 1.

Teacher's Note:
1. Eight drops have eight times the area of one small drop.
2. The big drop's area is only four times that of a small drop.

Answer: (a) 7.9 × 10⁻⁶ J

Explanation:
1. R = 10⁻³ m and the small drop radius r = 10⁻⁴ m.
2. Increase in area = 4π (1000 r² − R²) = 4π (10⁻⁵ − 10⁻⁶) = 1.13 × 10⁻⁴ m², so W = 7 × 10⁻² × 1.13 × 10⁻⁴ = 7.9 × 10⁻⁶ J.

Teacher's Note:
1. Cube root of 1000 gives the radius ratio 10.
2. Work is surface tension times the increase in area.

Answer: (d) 96 × 10⁻⁶ J

Explanation:
1. Increase in area = 32 − 16 = 16 cm² = 16 × 10⁻⁴ m².
2. A soap film has two surfaces, so W = 2 × 3 × 10⁻² × 16 × 10⁻⁴ = 96 × 10⁻⁶ J.

Teacher's Note:
1. Do not forget the factor 2 for the two faces of the film.
2. Convert cm² to m².

Answer: (d) 4^(1/3) W

Explanation:
1. Work is proportional to the surface area, which goes as R², that is V^(2/3).
2. For 2V the work is 2^(2/3) W = 4^(1/3) W.

Teacher's Note:
1. Volume goes as the cube of the radius, area as the square.
2. So area goes as V^(2/3).

Answer: (b) P1 = P2

Explanation:
1. An air bubble inside water has one liquid surface, so excess pressure = 2T/r.
2. A water drop in air also has one surface, so its excess pressure is 2T/r as well, and P1 = P2.

Teacher's Note:
1. Soap bubbles have two surfaces and 4T/r.
2. A bubble in a liquid and a drop of liquid each have one surface.

Answer: (a) 0.200 μm

Explanation:
1. Excess pressure 2T/r is inversely proportional to the radius.
2. It is largest for the smallest diameter, 0.200 μm.

Teacher's Note:
1. Smaller drops have a higher internal pressure.
2. Compare all the diameters in the same unit.

Answer: (b) 8 : 1

Explanation:
1. Excess pressure 4T/r is inversely proportional to r, so r_A = 2 r_B.
2. Volumes go as r³, so V_A : V_B = 8 : 1.

Teacher's Note:
1. Lower excess pressure means a bigger bubble.
2. Cube the radius ratio for volume.

Answer: (c) 13 cm

Explanation:
1. In vacuum there is no outside gas, so the surface area (surface energy) is conserved.
2. R² = r1² + r2² = 144 + 25 = 169, so R = 13 cm.

Teacher's Note:
1. For bubbles in vacuum, the sum of the surface areas is conserved.
2. This differs from the case of drops, where volume is conserved.

Answer: (b) obtuse (more than 90°)

Explanation:
1. A liquid wets a surface when the angle of contact is acute.
2. It does not wet the surface when the angle is obtuse, as for mercury on glass.

Teacher's Note:
1. Obtuse contact angle gives a convex meniscus and capillary fall.
2. Acute contact angle gives a concave meniscus and capillary rise.

Answer: (c) 3 : 1

Explanation:
1. Height of rise h is inversely proportional to the radius.
2. r1 / r2 = h2 / h1 = 66 / 22 = 3 (the tube with the smaller rise is the wider one), so the ratio is 3 : 1.

Teacher's Note:
1. The narrower tube has the greater capillary rise.
2. Compare radii as the inverse of the heights.

Answer: (d) more than the atmospheric pressure

Explanation:
1. Mercury has a convex meniscus (obtuse contact angle).
2. The pressure on the concave side, just below the meniscus, is greater than atmospheric pressure, which pushes the mercury down in the tube.

Teacher's Note:
1. The pressure is higher on the concave side of a curved liquid surface.
2. This is why a convex meniscus gives capillary fall.

Answer: (b) 15 cm

Explanation:
1. Water does not leak while ρ g h is not greater than the excess pressure of the curved surface, 2T/r.
2. h = 2T/(r ρ g) = 2 × 75 / (0.01 × 1 × 1000) = 15 cm.

Teacher's Note:
1. The surface film in the hole acts like a curved membrane.
2. Use CGS units throughout: r = 0.01 cm.

Answer: (d) full length of the capillary tube

Explanation:
1. In a satellite the effective gravity is zero (weightlessness).
2. Since h = 2T cos θ / (r ρ g) becomes infinite, the water rises to fill the entire tube.

Teacher's Note:
1. Capillary rise is balanced only by weight.
2. With no weight, nothing stops the rise.

Answer: (a) 6h

Explanation:
1. h = 2T cos θ / (r ρ g) is inversely proportional to g.
2. With g one-sixth, the height is 6h.

Teacher's Note:
1. Capillary rise depends on gravity.
2. It does not depend on the mass of the liquid.

Answer: (d) 500 N/m

Explanation:
1. The weight of the liquid column is balanced by the surface tension force, W = 2π r T cos θ.
2. T = 6.2 / (2π × 0.2 × 10⁻²) ≈ 493 N/m, which is nearest to 500 N/m.

Teacher's Note:
1. The force acts along the circumference 2πr.
2. The value obtained is unusually large, but it is the nearest option.

Answer: (a) 12.5 × 10⁻² m

Explanation:
1. The upward force is T × (circumference) = weight.
2. Circumference = 75 × 10⁻⁴ / (6 × 10⁻²) = 12.5 × 10⁻² m.

Teacher's Note:
1. For zero contact angle the surface tension force acts vertically along the full circumference.
2. The force is T times the length of the contact line.

Answer: (b) 2 cm

Explanation:
1. h = 2T cos θ / (r ρ g) = 2 × 70 / ((1/14) × 1 × 980).
2. = 140 × 14 / 980 = 2 cm.

Teacher's Note:
1. Use CGS units and density 1 g/cm³ for water.
2. Dividing by 1/14 is multiplying by 14.

Answer: (a) 8/√3 cm

Explanation:
1. The vertical height of the water column stays 4 cm.
2. Length along the tube = 4 / cos 30° = 4 / (√3/2) = 8/√3 cm.

Teacher's Note:
1. Capillary rise is a vertical height.
2. Tilting only lengthens the column along the tube.

Answer: (b) 0.07 mm

Explanation:
1. Water just enters when ρ g h = 2T/r.
2. r = 2 × 0.07 / (1000 × 10 × 0.4) = 3.5 × 10⁻⁵ m, so the diameter is 7 × 10⁻⁵ m = 0.07 mm.

Teacher's Note:
1. The hole acts like a capillary opening that resists the pressure by surface tension.
2. Take the diameter, not the radius, as the answer.

Answer: (a) angle of contact between the surface and the liquid

Explanation:
1. A liquid wets a surface if the angle of contact is acute and does not if it is obtuse.
2. So wettability depends mainly on the angle of contact.

Teacher's Note:
1. The angle of contact depends on the combination of liquid, solid and surrounding gas.
2. It decides whether the meniscus is concave or convex.

Answer: (c) water rises up to the top of the capillary tube and stays there without overflowing

Explanation:
1. The radius of curvature of the meniscus adjusts so that the pressure difference 2T/R balances the smaller column h' ρ g.
2. The meniscus becomes flatter, and the water stays at the top without overflowing.

Teacher's Note:
1. Surface tension cannot supply energy for a fountain.
2. The meniscus becomes less curved to balance the smaller column.

Answer: (d) 0.125 N m⁻¹

Explanation:
1. The increase in area = 20 − 8 = 12 cm² = 12 × 10⁻⁴ m², and the film has two surfaces.
2. W = 2 T ΔA gives T = 3 × 10⁻⁴ / (2 × 12 × 10⁻⁴) = 0.125 N/m.

Teacher's Note:
1. Use two surfaces for a liquid film.
2. Convert cm² to m².