Question

Modulus of rigidity of ideal liquids is
A. infinity
B. zero
C. unity
D. some finite small non-zero constant value

Answer 1

Hint: We will define the term ideal liquids first, then will continue with the discussion of the modulus of rigidity. We will make use of the formulae that relate the modulus of rigidity, stress and strain. Thus, by knowing the formula of the modulus of rigidity, we can find the modulus of rigidity of the ideal liquids.

Formula used:
\[\eta =\dfrac{\text{stress}}{\text{strain}}\]

Complete answer:
The modulus of rigidity is the ratio of the tangential stress to the shearing strain. The formula that defines the relationship between the modulus of rigidity, stress and strain is given as follows.

\[\eta =\dfrac{\text{stress}}{\text{strain}}\]

Where \[\eta \]is the modulus of rigidity.

The features of the ideal liquid are as follows.

No frictional force will be present in the case of ideal liquids.

As no stress develops in the ideal gas, thus, no tangential force will occur.

Even the modulus of rigidity will not be present, because of the following.

We will make use of the formulae that relate the modulus of rigidity, stress and strain. Consider the formula and substitute the value of stress.

\[\begin{align}
  & \eta =\dfrac{\text{0}}{\text{strain}} \\
 & \Rightarrow \eta =0 \\
\end{align}\]

 \[\therefore \] The modulus of rigidity of the ideal gas will be zero.

As, the value of the modulus of the rigidity of the ideal gas is zero, thus, the option (B) is correct.

Note:
The modulus of rigidity is different for different forms of matter, that is, solid, liquid and gas. As in this case, we have discussed the formula to define the modulus of rigidity as per stress and the strain, similarly, when asked for this type of question, the same method should be followed.