Assertion (A): Identical springs of steel and copper are equally stretched. More work will be done on the steel spring.
Reason (R): Steel is more elastic than copper.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true. Work done to stretch a spring is \(W = \frac{1}{2} k x^2\). Steel has a higher Young's modulus than copper, implying a higher spring constant \(k\) for identical dimensions.
Thus, more work is done on the steel spring.
Reason (R) is true. Steel is indeed more elastic than copper (possesses a higher Young's modulus).
Reason (R) correctly explains Assertion (A).
Assertion (A): A raindrop after falling through some height attains a constant velocity.
Reason (R): At constant velocity the viscous drag plus buoyant force is just equal to its weight.
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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Assertion (A) is true, as falling objects in a fluid reach terminal velocity when resistive forces balance gravity.
Reason (R) is true, stating the force balance condition for constant velocity: Weight = viscous drag + buoyant force. (R) correctly explains (A).
Assertion (A): In streamline flow streamlines never intersect each other.
Reason (R): If streamline intersect then their must two velocities of fluid particle at the point of intersection, which is impossible.
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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Assertion (A) is true by definition of streamline flow.
Reason (R) is true because intersection would imply multiple velocity vectors at a single point, which is physically impossible.
(R) correctly explains (A).
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): 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.