Question

For an ideal liquid:
A. bulk modulus is zero and shear modulus is infinite.
B. bulk modulus is infinite and shear modulus is zero.
C. bulk modulus is infinite and shear modulus is also infinite.
D. bulk modulus is zero and shear modulus is also zero.

Answer 1

An ideal fluid has zero viscosity, and it is incompressible. Bulk modulus is the ratio of applied pressure to change in volume. Also, shear modulus is the ratio of shear force to the shear strain.
For ideal liquids, the change in volume is zero and shear stress is infinite.

Complete step-by-step answer:
An ideal liquid is one that is incompressible and has no viscosity. In actuality, these do not exist. It is imaginary fluid and exists in only theories.
Now, the bulk modulus is the measure of the resistance of the fluid to compression. It is the ratio of applied pressure to the change in volume. It is used to measure the incompressibility of the liquid.
As the pressure applied is the ratio of force per unit area, given as:$P=F/A$
Then the bulk modulus is given by;
$\begin{aligned} & B=P/(\vartriangle V/V) \\\ & \Rightarrow B=(F/A)/(\vartriangle V/V) \\\ \end{aligned}$
Now the ideal liquid is Incompressible, so the change in volume is zero.
So, the bulk modulus is infinite.
Now, the shear strain deals with the deformation of the object. The shear modulus is the elastic modulus. Shear stress acts on two parallel surfaces of the objects. Strain deals force act on the object to cause the change of length.
Now the shear modulus (S.M) is the ratio of shear force to the shear strain. Mathematically:
$S.M=(f/A)/(x/y)$
The shear force is the ratio of force per unit area. So, in case of ideal liquids the shear strain is infinite.
$\begin{aligned} & G=(force/area)/(shear strain) \\\ & \Rightarrow G=(force/area)/\infty \\\ & \therefore G=0 \\\ \end{aligned}$
Therefore, the shear modulus is zero.

So, the correct answer is “Option B”.

Note: An ideal liquid is imaginary liquids and exists only in theory. It is incompressible, and has zero viscosity. Bulk modulus depends inversely on the change in volume, and change in volume for ideal liquids is zero, so it is infinite. Also shear modulus depends on the shear strain which is infinite and hence the shear modulus is zero.