The bulk modulus of water is 2.1 ×10^9 N / m^2. The pressure required to increase the density o

Name: Problem 32, Chapter 15: Arihant AIEEE Physics
Uploaded: 2021-09-19T14:47:36-08:00
Duration: 1 min 25 s
Channel: Ajay Singhal
Description: The bulk modulus of water is 2.1 ×10^9 N / m^2. The pressure required to increase the density of water by 0.1 % is : (a) 2.1 ×10^3 N / m^2 (b) 2.1 ×10^6 N / m^2 (c) 2.1 ×10^5 N / m^2 (d) 2.1 ×10^2 N / m^2

step 1 Hello, students. In this question, we have given the bulk modulus of water is 2 .1 into 10 to th

Question

The bulk modulus of water is $2.1 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. The pressure required to increase the density of water by $0.1 \%$ is : (a) $2.1 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$ (b) $2.1 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ (c) $2.1 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ (d) $2.1 \times 10^{2} \mathrm{~N} / \mathrm{m}^{2}$

   The bulk modulus of water is $2.1 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. The pressure required to increase the density of water by $0.1 \%$ is :
(a) $2.1 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$
(b) $2.1 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(c) $2.1 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
(d) $2.1 \times 10^{2} \mathrm{~N} / \mathrm{m}^{2}$

Arihant AIEEE Physics

D.B. Singh 2006 Edition

Chapter 15, Problem 32

Instant Answer

Solved by Expert Ajay Singhal

09/19/2021

Step 1

1 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ and we need to find the pressure required to increase the density of water by $0.1 \%$. Show more…

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The bulk modulus of water is $2.1 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. The pressure required to increase the density of water by $0.1 \%$ is : (a) $2.1 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$ (b) $2.1 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ (c) $2.1 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ (d) $2.1 \times 10^{2} \mathrm{~N} / \mathrm{m}^{2}$

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Key Concepts

Pressure-Density Relationship

In fluids, there is a direct relationship between changes in pressure and changes in density, governed by the bulk modulus. For small deformations, the fractional increase in density is approximately equal to the increase in pressure divided by the bulk modulus. This linear relationship allows for the calculation of the pressure needed to achieve a specific percentage change in density.

Bulk Modulus

The bulk modulus is a measure of a material's resistance to uniform compression. It quantifies how much pressure must be applied to a material to produce a given fractional change in volume (or inversely, density). In fluids like water, a higher bulk modulus indicates that the fluid is less compressible, meaning that even large increases in pressure result in only small changes in volume or density.

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