(B) The density $\rho$ is given by $\rho = \frac{M}{V}$,where $M$ is the mass and $V$ is the volume.Taking the logarithmic derivative,we get $\frac{d\

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) The density $\rho$ is given by $\rho = \frac{M}{V}$,where $M$ is the mass and $V$ is the volume.Taking the logarithmic derivative,we get $\frac{d\rho}{\rho} = -\frac{dV}{V}$.The bulk modulus $K$ is defined as $K = -\frac{P}{dV/V}$,which implies $-\frac{dV}{V} = \frac{P}{K}$.Substituting this into the density relation,we get $\frac{d\rho}{\rho} = \frac{P}{K}$.Therefore,the magnitude of the increase in density is $d\rho = \frac{\rho P}{K}$.

Class 11 Physics Mechanical Properties of Solids Bulk Modulus

Medium

The normal density of a material is $\rho$ and its bulk modulus of elasticity is $K$. The magnitude of increase in density of the material,when a pressure $P$ is applied uniformly on all sides,will be

JEE MAIN 2021 All JEE MAIN

AIIMS 2017 All AIIMS

A
$\frac{\rho K}{P}$
B
$\frac{\rho P}{K}$
C
$\frac{K}{\rho P}$
D
$\frac{PK}{\rho}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Mechanical Properties of Solids

Subtopic

Bulk Modulus

Previous Year

JEE MAIN 2021 Paper All JEE MAIN years →

Previous Year

AIIMS 2017 Paper All AIIMS years →

$A$ copper solid cube of $60\, mm$ side is subjected to a pressure of $2.5 \times 10^7\, Pa$. If the bulk modulus of copper is $1.25 \times 10^{11}\, N/m^2$,the change in the volume of the cube is:

Medium

View Solution

$A$ ball falling in a lake of depth $200 \ m$ shows $0.1\%$ decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

Medium

View Solution

How much should the pressure on a litre of water be changed to compress it by $0.10\%?$

Easy

View Solution

$A$ spherical ball contracts in volume by $0.02 \%$,when subjected to a normal uniform pressure of $50$ atmosphere. The Bulk modulus of its material is ............... $N / m^2$.

Easy

View Solution

$A$ glass slab is subjected to a pressure of $10 \, atm$. The fractional change in its volume is (Bulk modulus of glass $= 37 \times 10^9 \, N \, m^{-2}$,$1 \, atm = 1 \times 10^5 \, N \, m^{-2}$)

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The normal density of a material is $\rho$ and its bulk modulus of elasticity is $K$. The magnitude of increase in density of the material,when a pressure $P$ is applied uniformly on all sides,will be

Similar Questions

$A$ copper solid cube of $60\, mm$ side is subjected to a pressure of $2.5 \times 10^7\, Pa$. If the bulk modulus of copper is $1.25 \times 10^{11}\, N/m^2$,the change in the volume of the cube is:

$A$ ball falling in a lake of depth $200 \ m$ shows $0.1\%$ decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

How much should the pressure on a litre of water be changed to compress it by $0.10\%?$

$A$ spherical ball contracts in volume by $0.02 \%$,when subjected to a normal uniform pressure of $50$ atmosphere. The Bulk modulus of its material is ............... $N / m^2$.

$A$ glass slab is subjected to a pressure of $10 \, atm$. The fractional change in its volume is (Bulk modulus of glass $= 37 \times 10^9 \, N \, m^{-2}$,$1 \, atm = 1 \times 10^5 \, N \, m^{-2}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module