(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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The increase in the pressure required to decrease the volume $(\Delta V)$ of water is $6.3 \times 10^7 \text{ N/m}^2$. The percentage decrease in the volume is . . . . . . . (Bulk modulus of water = $2.1 \times 10^9 \text{ N/m}^2$.) (in $\%$)

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The average depth of the Indian Ocean is about $3000\; m$. Calculate the fractional compression,$\Delta V / V,$ of water at the bottom of the ocean,given that the bulk modulus of water is $2.2 \times 10^{9}\; N m^{-2}$. (Take $g = 10\; m s^{-2}$)

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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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The fractional change in the volume of a glass slab when subjected to a hydraulic pressure of $14 \,atm$ is (Bulk modulus of glass $= 40 \times 10^9 \,N/m^2$).

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What is compressibility? Give its unit and dimensional formula.

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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

Similar Questions

The increase in the pressure required to decrease the volume $(\Delta V)$ of water is $6.3 \times 10^7 \text{ N/m}^2$. The percentage decrease in the volume is . . . . . . . (Bulk modulus of water = $2.1 \times 10^9 \text{ N/m}^2$.) (in $\%$)

The average depth of the Indian Ocean is about $3000\; m$. Calculate the fractional compression,$\Delta V / V,$ of water at the bottom of the ocean,given that the bulk modulus of water is $2.2 \times 10^{9}\; N m^{-2}$. (Take $g = 10\; m s^{-2}$)

$A$ 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:

The fractional change in the volume of a glass slab when subjected to a hydraulic pressure of $14 \,atm$ is (Bulk modulus of glass $= 40 \times 10^9 \,N/m^2$).

What is compressibility? Give its unit and dimensional formula.

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