Question

If $B$ is the bulk modulus of a metal and a pressure $P$ is applied uniformly on all sides of the metal with density $D$, then the fractional increase in density is given by (a) $\frac{B}{P}$ (b) $\frac{P}{B}$ (c) $\frac{P D}{B}$ (d) $\frac{B D}{P}$

Name: Problem 2, Chapter 9: Objective Physics for NEET
Uploaded: 2021-09-18T16:58:48-08:00
Duration: 3 min
Channel: Dheeraj Sharma
Description: If B is the bulk modulus of a metal and a pressure P is applied uniformly on all sides of the metal with density D, then the fractional increase in density is given by (a) (B)/(P) (b) (P)/(B) (c) (P D)/(B) (d) (B D)/(P)

   If $B$ is the bulk modulus of a metal and a pressure $P$ is applied uniformly on all sides of the metal with density $D$, then the fractional increase in density is given by
(a) $\frac{B}{P}$
(b) $\frac{P}{B}$
(c) $\frac{P D}{B}$
(d) $\frac{B D}{P}$

Objective Physics for NEET

Abhay Kumar 1st Edition

Chapter 9, Problem 2

Instant Answer

Solved by Expert Dheeraj Sharma

09/18/2021

Step 1

Step 1: The density $D$ is given by $D = \frac{M}{V}$, where $M$ is the mass and $V$ is the volume. Show more…

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If $B$ is the bulk modulus of a metal and a pressure $P$ is applied uniformly on all sides of the metal with density $D$, then the fractional increase in density is given by (a) $\frac{B}{P}$ (b) $\frac{P}{B}$ (c) $\frac{P D}{B}$ (d) $\frac{B D}{P}$

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Key Concepts

Bulk Modulus

The bulk modulus of a material is a measure of its resistance to uniform compression. It is defined as the ratio of the applied pressure increase to the resulting relative decrease in volume. This property is fundamental in understanding how materials compress under pressure and directly relates to their stiffness in response to isotropic stress.

Volume Strain and Its Relationship to Density

Volume strain refers to the relative change in a material's volume under stress. Since density is mass per unit volume and the mass remains constant during compression, any decrease in volume results in a corresponding increase in density. The fractional increase in density is directly linked to the reduction in volume, making the understanding of volume strain essential in problems involving compressibility.

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