Question

The bulk modulus for an incompressible liquid is?
A. Zero
B. unity
C. Infinity
D. Between 0 and 1

Answer 1

- Hint: In order to solve this problem we need to use the formula of bulk modulus and observe the situation that when an incompressible liquid is taken under consideration then what would be the value of the terms present over there. Doing this will solve our problem and we will get the right answer.

Complete step-by-step solution -

Bulk Modulus - Also referred to as incompressibility, the bulk modulus is a measure of the ability of a material to tolerate changes in volume when under compression on all sides. It is equal to the quotient of the applied pressure which is divided by the relative deformation.
Bulk modulus is denoted as $K = \dfrac{{ - dP}}{{\dfrac{{dV}}{V}}} = \dfrac{{ - VdP}}{{dV}}$.
dP is change in pressure and dV is change in volume.
V is volume.
We know that the change in volume dV is zero for incompressible liquid.
So, the denominator of the formula of bulk modulus $K = \dfrac{{ - dP}}{{\dfrac{{dV}}{V}}} = \dfrac{{ - VdP}}{{dV}}$ is zero.
So the value of Bulk modulus K will be very close to infinity. So, the answer to this problem is infinity.
Hence, the correct option is C.

Note – In this problem you just need to recall the basic formula of bulk modulus and observe the change in volume when the liquid is incompressible. Such problems generally arise in competitive exams in which you have to use the formula of the term and have to give the answer according to that formula. Bulk Modulus is a constant that defines how resistant the material is to compression. It is defined as the ratio between the increase in pressure and the resulting decrease in the volume of the material. The density of the material is the degree of compactness of the material. This is known as the mass per unit volume.