Question

With increase in pressure, the bulk modulus of elasticity
A. Increases
B. Decreases
C. Remains constant
D. Increases and decreases

Answer 1

Hint: Bulk modulus of elasticity is defined as the ratio of change or decrease in volume, when pressure of a material is increased. In other words, it shows the incompressibility of a substance. It is denoted by the symbol $k$.

Complete step by step solution:
Bulk modulus is the property of materials (solids, liquids or gases) which is used to measure the extent of deformation of a substance, when and if stress is applied on the substance. The stress applied is within the elastic limit of that material. It is usually greater than zero. It is given by the units ‘Pascal’ or ‘Newton per metre square’. It is a constant numeric number, which is used to represent the deformation or compression of any solid, liquid or gas, when pressure is applied.

As the expression of Bulk modulus of elasticity is given as,
$k=\dfrac{\text{stress}}{\text{strain}}=\dfrac{-dp}{\dfrac{dV}{V}}$
When the pressure on a material is increased, the bulk modulus of elasticity for the material also increases. This is because when pressure is increased, the molecules of the substance come together and the volume of the material decreases. The molecules try to resist the deformation in change of the shape as volumetric strain is applied across the material. Therefore, a large pressure is to be applied on that material.

Therefore, option A is the correct answer.

Note: The reciprocal of bulk modulus of elasticity is also known as compressibility. It is the compressibility which shows by how much is any material compressed when pressure is applied on it externally. That means if a substance has a small value of compressibility, then its bulk modulus is large.