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Chapter 7: Problem 1023

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: The water rises higher in a capillary tube of small diametre than in the capillary tube of large diameter. Reason: Height through which liquid rises in a capillary tube is inversely proportional to the diameter of the capillary tube. (A) a (B) b (C) c (D) d

Short Answer

Expert verified
\( \boxed{A} \)

Step by step solution

01

1. Check the correctness of the assertion

To verify the assertion, let's remember the behavior of liquids in capillary tubes. Capillary action is the result of surface tension and adhesion forces between the liquid and the tube walls. The liquid rises or falls inside the tube until the weight of the liquid column is balanced by the adhesive forces acting on the surface. In narrow tubes (small diameter), the water can rise higher than in wide tubes (large diameter) due to these adhesive forces. So, the assertion is true.
02

2. Check the correctness of the reason

The height to which the liquid rises in a capillary tube can be described using Jurin's law that states: \[ h = \dfrac{2\gamma\cos\theta}{\rho gr} \] where h is the height of the liquid column, γ (gamma) is the surface tension of the liquid, θ (theta) is the contact angle between the liquid and the tube walls, ρ (rho) is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the capillary tube. This shows that the height of the liquid rise in the capillary tube is indeed inversely proportional to the diameter (and radius) of the tube. Thus, the reason is also true.
03

3. Determine if the reason is the correct explanation of the assertion

Since the reason successfully explains the mathematical relationship between the height of liquid rise and the diameter of the capillary tube, it adequately provides the correct explanation for the assertion. Therefore, the reason supports and correctly explains the assertion. Now, we can choose the correct option based on our analysis of the given statements: (A) a Since both the assertion and reason are true, and the reason is the correct explanation of the assertion, the correct answer is: (A) a.

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Most popular questions from this chapter

A beaker of radius \(15 \mathrm{~cm}\) is filled with liquid of surface tension \(0.075 \mathrm{~N} / \mathrm{m}\). Force across an imaginary diameter on the surface of liquid is (A) \(0.075 \mathrm{~N}\) (B) \(1.5 \times 10^{-2} \mathrm{~N}\) (C) \(0.225 \mathrm{~N}\) (D) \(2.25 \times 10^{-2} \mathrm{~N}\)

The force required to separate two glass plates of area $10^{-2} \mathrm{~m}^{2}\( with a film of water \)0.05 \mathrm{~mm}$ thick between them is (surface tension of water is \(70 \times 10^{-3} \mathrm{~N} / \mathrm{m}\) ) (A) \(28 \mathrm{~N}\) (B) \(14 \mathrm{~N}\) (C) \(50 \mathrm{~N}\) (D) \(38 \mathrm{~N}\)

Radius of a soap bubble is \(\mathrm{r}^{\prime}\), surface tension of soap solution is \(\mathrm{T}\). Then without increasing the temperature how much energy will be needed to double its radius. (A) \(4 \pi r^{2} T\) (B) \(2 \pi r^{2} T\) (C) \(12 \pi r^{2} T\) (D) \(24 \pi r^{2} T\)

Eight drops of a liquid of density 3 and each of radius a are falling through air with a constant velocity \(3.75 \mathrm{~cm} \mathrm{~S}^{1}\) when the eight drops coalesce to form a single drop the terminal velocity of the new drop will be (A) \(15 \times 10^{-2} \mathrm{~ms}^{-1}\) (B) \(2.4 \times 10^{-2} \mathrm{~m} / \mathrm{s}\) (C) \(0.75 \times 10^{-2} \mathrm{~ms}^{-1}\) (D) \(25 \times 10^{-2} \mathrm{~m} / \mathrm{s}\)

The work done increasing the size of a soap film from $10 \mathrm{~cm} \times 6 \mathrm{~cm}\( to \)10 \mathrm{~cm} \times 11 \mathrm{~cm}\( is \)3 \times 10^{-4}$ Joule. The surface tension of the film is (A) \(1.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (B) \(3.0 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (C) \(6.0 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (D) \(11.0 \times 10^{-2} \mathrm{~N} / \mathrm{m}\)
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