Question

Young’s modulus of perfectly rigid body material is:
A. Infinite
B. Zero
C. $10 \times {10^{10}}N/{m^2}$
D. $1 \times {10^{10}}N/{m^2}$

Answer 1

Hint:We know that the Young’s modulus is defined as the ratio of stress and strain of a material on which some kind of force is applied. Therefore, to solve this question we need to know the concept of stress and stress. After that, we need to consider the case of rigid body and stress and stress when the force is applied on this rigid body to get the final answer.

Formula used:
$Y = \dfrac{\sigma }{\delta }$
where, $Y$ is the young's modulus, $\sigma$ is the stress and $\delta$ is the strain.

Complete step by step answer:
We will first see the concepts of stress and strain. Stress can be defined as the force applied per unit area and strain can be defined as the ratio of change in length to the original length.Now, the rigid body can be defined as the body in which there is no deformation or a very small deformation which can be neglected. Therefore, we can say that when any force is applied in the rigid body, there will be stress.

However, for a perfectly rigid body, there is no change in the length of the body. As a result, the strain on the perfectly rigid body will be zero.If we put strain value zero in the formula $Y = \dfrac{\sigma }{\delta }$ , we will get the value of Young’s modulus as infinite.Thus, the Young’s modulus of perfectly rigid body material is infinite.

Hence, option A is the right answer.

Note:Here we have seen that the Young’s modulus of perfectly rigid body material is infinite. However in actual condition, perfectly rigid body material does not exist. There are always some changes in length of the material when the force is applied on it. These changes may be either in the direction of applied force or in the perpendicular direction of the applied force.