Question

Which of the following statement is wrong
A.Young’s modulus for perfectly rigid body is zero
B.Bulk modulus is defined for solids, liquids and gases
C.Rubber is less elastic than steel
D.The stretching of a coil spring is determined by its shear modulus.

Answer 1

The above problem can be resolved by remembering the basics of elasticity which says that young’s modulus is the ratio or the fraction of stress and strain and for a rigid body, there will be almost no change in its dimensions when a stress applied to them.

Complete answer:
The young’s modulus of a rigid body is given as:
$Y=\dfrac{\sigma }{\varepsilon }$
Here $\sigma$ is the stress applied on the body while $\varepsilon$ is the strain produced in the body. Now strain can be defined as:
$\varepsilon =\dfrac{\Delta L}{L}$
Which means that strain is the ratio of change in length $\left( \Delta L \right)$ and the original length $\left( L \right)$ of the body. For perfectly rigid bodies, there will be no change in length i.e., $\Delta L=0$ and hence the strain will be zero. If strain is zero, then the value of young’s modulus will be:
$\begin{aligned} & Y=\dfrac{\sigma }{0} \\\ & \therefore Y\to \infty \\\ \end{aligned}$
Therefore, young’s modulus for perfectly rigid bodies will be infinity, hence option $A$ is the answer.
Bulk modulus is the ratio of the change in volume of a body and its original volume in solids, liquids and gases. Hence statement $B$ is correct.
Rubber is less elastic than steel because steel has a higher value of young’s modulus due to which the amount of strain produced for a particular stress is less in steel as compared to that in rubber. Hence the statement $C$ is correct.
Stretching of a coil is determined by its shear modulus because only the shape of the coil is changed but not its length. Hence the statement $D$ is correct.

Note:
From the above explanation we can conclude that statement $A$ is incorrect, hence the answer is option $A$, because the young’s modulus for perfectly rigid bodies is infinity because the denominator of young’s modulus becomes zero, while for perfectly non-rigid bodies it is zero.