Question

The modulus of rigidity of ideal liquid is
(A) Infinity
(B) Zero
(C) Unity
(D) Some finite non-zero constant value

Answer 1

Hint : Modulus of rigidity can be defined as the ratio of shear stress to shear strain in a body. It is the measure of the rigidity of the body, it is often used for solids. Ideal liquid has no friction and thus no tangential force acts on it.

Complete step by step answer
Modulus of rigidity is defined as the ratio of shear stress to shear strain. Shear stress simply means the tangential force on a body that tends to change the shape of the body. Shear strain can be understood simply as deformation of the body in the direction parallel to the applied stress.
Mathematically,
 $\Rightarrow \eta = \dfrac{{\dfrac{F}{A}}}{{\dfrac{{\Delta x}}{l}}} $
 $\Rightarrow \eta = \dfrac{{Fl}}{{A\Delta x}} $ $ - - - - (1) $
Where, $ \dfrac{F}{A} $ is the shear stress, $ \Delta x $ is the transverse displacement,
 $ l $ is the initial length of the body.
 $ \therefore \dfrac{{\Delta x}}{l} $ is the shear strain.
As we know that, while considering ideal liquid there are some assumptions. One of them is that there is no frictional force present in the case of ideal liquids. This implies that there is no tangential force.
From the equation $ (1) $ , we can conclude that zero tangential force means zero modulus of rigidity.
Thus, option (B) is correct.

Additional Information
In the case of solids, there is the presence of frictional force, if a very strong tangential force is acting on it. It will lead to the deformation of the solid along the direction of the force. Thus it will have some non-zero finite value for modulus of rigidity, unlike ideal liquid.

Note
To solve such a problem, you need to have a complete idea of the ideal liquid and how it is defined theoretically. It is important to understand the concept because problems based on properties of ideal liquid can be framed in this way.