Assertion (A): Water flows faster than honey.
Reason (R): The co-efficient of viscosity of water is less than honey.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: Viscosity and fluid resistance. Viscosity is a measure of a fluid's resistance to flow. A fluid with lower viscosity flows more easily and thus faster. Water has a significantly lower coefficient of viscosity than honey. Both Assertion and Reason are true, and Reason correctly explains Assertion.
Assertion (A): The angle of contact of a liquid decreases with increase in temperature.
Reason (R): With increase in temperature, the surface tension of liquid increases.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: Effect of temperature on liquid properties. Assertion (A) is true; generally, the angle of contact decreases with increasing temperature as intermolecular forces weaken. Reason (R) is false; surface tension of a liquid *decreases* with an increase in temperature, not increases, because the kinetic energy of molecules increases, reducing cohesive forces.
Assertion (A): The shape of a liquid drop is spherical.
Reason (R): The pressure inside the drop is greater than that of outside.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: Surface tension and pressure difference. Assertion (A) is true because surface tension tends to minimize the surface area of a liquid for a given volume, and a sphere has the minimum surface area. Reason (R) is true; due to surface tension, there is an excess pressure inside a spherical liquid drop, given by \(P_{in} - P_{out} = \frac{2T}{R}\). This excess pressure balances the inward pull of surface tension, thus R correctly explains A.
Assertion (A): Surface energy of an oil drop is same whether placed on glass or water surface.
Reason (R): Surface energy is dependent only on the properties of oil.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: Interfacial surface energy. Surface energy (or surface tension) is a property of the interface between two phases. It depends on the intermolecular forces between the molecules of *both* substances forming the interface. Therefore, an oil-glass interface will have different surface energy than an oil-water interface. Both Assertion and Reason are false.
The viscous drag acting on a metal sphere of diameter \(1 \text{mm}\), falling through a fluid of viscosity \(0.8 \text{Pa} \text{s}\) with a velocity of \(2 \text{m} \text{s}^{-1}\) is equal to
1. \(1.5 \times 10^{-3} \text{N}\)
2. \(20 \times 10^{-3} \text{N}\)
3. \(15 \times 10^{-3} \text{N}\)
4. \(30 \times 10^{-3} \text{N}\)
View Answer
Using Stokes' Law: \(F = 6\pi\eta r v\). Here, \(r = 0.5 \times 10^{-3} \text{m}\), \(\eta = 0.8 \text{Pa} \text{s}\), and \(v = 2 \text{m/s}\). \(F = 6 \times \pi \times 0.8 \times 0.5 \times 10^{-3} \times 2 \approx 15 \times 10^{-3} \text{N}\).
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Strain is a dimensionless quantity.
Reason R: Unit of Young’s modulus is same as that of stress.
In the light of the above statements, choose the correct answer from the option given below.
1. Both A and R are true and R is the correct explanation of A
2. Both A and R are true but R is not the correct explanation of A
3. A is true but R is false
4. A is false but R is true
View Answer
Strain is indeed dimensionless since it's the ratio of two similar physical quantities (change in dimension over original dimension). The unit of Young's modulus is indeed identical to stress (both are \(\text{N/m}^2\)). However, the second statement is not the reason for the first.
Two copper vessels A and B have the same base area but of different shapes. Vessel A takes twice the volume of water as that vessel B requires to fill upto common particular height. Then correct statement among the following is
1. Force due to liquid on base of vessel A is more
2. Force due to liquid on base of vessel B is more
3. Pressure at base of vessel A is more
4. Pressure at base of both the vessels is same
View Answer
Liquid pressure at the base depends only on height and density of the liquid, \(P = \rho g h\). Since height is the same, pressure at the base of both vessels is the same.
Eight drops of equal radii are falling through air with a steady velocity of \(3\text{ cm/s}\). If the eight drops combine to form a single drop, then its steady velocity will be
1. \(3\text{ cm/s}\)
2. \(12\text{ cm/s}\)
3. \(6\text{ cm/s}\)
4. \(24\text{ cm/s}\)
View Answer
Terminal velocity \(v \propto r^2\). Since volume remains constant, \(\frac{4}{3}\pi R^3 = 8 \times \frac{4}{3}\pi r^3 \implies R = 2r\). Thus, the new terminal velocity is \(v' = \left(\frac{R}{r}\right)^2 v = 2^2 \times 3 = 12\text{ cm/s}\).
The experiment which is used to determine Young’s modulus of the material of a given wire, is
1. Resonance tube experiment
2. Displacement method
3. Searle's experiment
4. Young's double slit experiment
View Answer
Searle's apparatus/experiment is specifically designed and used to determine the Young's modulus of elasticity of a metal wire by measuring elongation under load.