(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\

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(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

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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

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

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Mechanical Properties of Solids

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Bulk Modulus

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$A$ 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:

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When a pressure of $100 \, atm$ is applied to a rubber ball,its volume decreases by $0.01 \%$. What is the bulk modulus of the rubber?

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$A$ spherical ball contracts in volume by $0.02 \%$, when subjected to a normal uniform pressure of $50 \text{ atm}$. The Bulk modulus of its material is ............. $Nm^{-2}$. (Take $1 \text{ atm} = 1.01 \times 10^5 \text{ Pa}$)

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The density of a metal at normal pressure is $\rho$. Its density when it is subjected to an excess pressure $p$ is $\rho^{\prime}$. If $B$ is the Bulk modulus of the metal,the ratio $\frac{\rho^{\prime}}{\rho}$ is:

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It is found that an increase in pressure of $100 \, kPa$ causes a certain volume of water to decrease by $5 \times 10^{-3}$ percent of its original volume. Then the speed of sound in the water is about .... $m/s$ (density of water $10^3 \, kg/m^3$)

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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

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$A$ 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:

When a pressure of $100 \, atm$ is applied to a rubber ball,its volume decreases by $0.01 \%$. What is the bulk modulus of the rubber?

$A$ spherical ball contracts in volume by $0.02 \%$, when subjected to a normal uniform pressure of $50 \text{ atm}$. The Bulk modulus of its material is ............. $Nm^{-2}$. (Take $1 \text{ atm} = 1.01 \times 10^5 \text{ Pa}$)

The density of a metal at normal pressure is $\rho$. Its density when it is subjected to an excess pressure $p$ is $\rho^{\prime}$. If $B$ is the Bulk modulus of the metal,the ratio $\frac{\rho^{\prime}}{\rho}$ is:

It is found that an increase in pressure of $100 \, kPa$ causes a certain volume of water to decrease by $5 \times 10^{-3}$ percent of its original volume. Then the speed of sound in the water is about .... $m/s$ (density of water $10^3 \, kg/m^3$)

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