Assertion (A): The stream of water emerging from a water tap “necks down” as it falls.
Reason (R): The volume flow rate at different levels is same.
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: Continuity equation for fluid flow. For an incompressible fluid in steady flow, the volume flow rate \(AV\) (Area × Velocity) must remain constant. As water falls, its velocity \(V\) increases due to gravity, therefore, its cross-sectional area \(A\) must decrease, causing it to 'neck down'. Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
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): Weight of an empty balloon measured in air is \(W_1\). If air at atmospheric pressure is filled inside balloon and again weight of the balloon is measured. Weight of balloon in second case is equal to \(W_1\).
Reason (R): Upthrust is equal to weight of the fluid displaced by the body.
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: Archimedes' Principle and apparent weight. When air at atmospheric pressure is filled into a balloon, the weight of the air inside is equal to the upthrust exerted by the surrounding air on the volume displaced by this internal air. Thus, the net change in apparent weight due to the air inside is zero. Both Assertion and Reason are true, and Reason explains Assertion by defining upthrust as per Archimedes' principle.
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.
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. \(30 \times 10^{-3} \text{N}\)
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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.