Question

Assertion – Young’s modulus for a perfectly plastic body is zero.
Reason – For a perfectly plastic body, restoring force is zero
$A)$ Both assertion and reason are correct and reason is the correct explanation for assertion.
$B)$ Both assertion and reason are correct but reason is not the correct explanation for assertion.
$C)$ Assertion correct but reason is incorrect.
$D)$ Both Assertion and reason is incorrect.

Answer 1

We will need hooke's law to solve this question. The law states that within elastic limit stress is directly proportional to strain. We must know that young’s modulus of a body measures the resistance of a material to the elastic deformation of that body under a force. Young’s modulus of a body relates stress to strain along an axis on a body. It is directly proportional to force per unit area acting on the body and inversely proportional to the deforming force. There will be a restoring force developed inside the body when a force is applied on it. This restoring force tries to bring the body into its equilibrium position. The Restoring force of a body is directly proportional to the displacement of the particle.

Complete step by step answer:
The assertion given in the question tells that young’s modulus of a perfectly plastic body is zero. If we need to determine the young’s modulus of a material, it is given by the expression,
$Y=\dfrac{\text{stress}}{\text{strain}}=\dfrac{F{{L}_{0}}}{A\Delta L}$
Where, $F$ is the force exerted by an object under pressure.
${{L}_{0}}$ is the actual length.
$A$ is the area of the cross section.
$\Delta L$ is the change in length.
We know a perfectly plastic body cannot regain its original shape when pressure is applied on it. That means the young’s modulus of a perfectly plastic body is zero.
So, the given assertion is a right statement.
Now, if we take the restoring force developed inside a perfectly plastic body, it is zero. This is the reason why these materials are not regaining their actual shape.
So the reason statement is also true and it is the correct reason for the assertion given.

So, the correct answer is “Option A”.

Note:
We must know that a perfectly plastic material is a hypothetical material that never tends to regain the original configuration on the removal of the deforming force. So, we cannot have a perfectly plastic body because this is only a theoretical concept. The deforming force in normal plastic bodies is not actually zero but there will be a small amount of restoring force present.