How much should the pressure on a litre of water be changed...

How much should the pressure on a litre of water be changed to compress it by $0.10 \% .$ Bulk modulus of elasticity of water $=2.2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. (a) $2.2 \times 10^{-6} \mathrm{~N}-\mathrm{m}^{-2}$ (b) $4.2 \times 10^{-6} \mathrm{~N}-\mathrm{m}^{-2}$ (c) $2.2 \times 10^{6} \mathrm{~N}-\mathrm{m}^{2}$ (d) $4.2 \times 10^{4} \mathrm{~N}-\mathrm{m}^{2}$

How much should the pressure on a litre of water be changed to compress it by $0.10 \% .$ Bulk modulus of elasticity of water $=2.2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$.
(a) $2.2 \times 10^{-6} \mathrm{~N}-\mathrm{m}^{-2}$
(b) $4.2 \times 10^{-6} \mathrm{~N}-\mathrm{m}^{-2}$
(c) $2.2 \times 10^{6} \mathrm{~N}-\mathrm{m}^{2}$
(d) $4.2 \times 10^{4} \mathrm{~N}-\mathrm{m}^{2}$

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Key Concepts

Bulk Modulus of Elasticity

The bulk modulus of elasticity is a material property that quantifies a substance's resistance to uniform compression. It is defined as the ratio of the applied pressure change to the resulting fractional change in volume. This concept is essential in understanding how compressible or incompressible a substance is under an external pressure.

Volume Strain

Volume strain is the measure of the fractional change in volume of a material when subjected to a pressure change. It is represented as (?V/V), where ?V is the change in volume and V is the original volume. This parameter indicates the extent of compression or expansion in a material.

Pressure-Volume Relationship

The pressure-volume relationship is the fundamental link between the change in pressure applied to a substance and its consequent volume change. This relationship, encapsulated in the equation ?P = Bulk Modulus × (?V/V), forms the basis of calculating the necessary pressure modification to achieve a desired level of compression in a material.

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