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Chapter 7: Problem 966

Assertion and Reason: Read the assertion and reason carefully to mark the correct option out of the option given below (A) If both assertion and reason are true and reason is the correct explanation of the assertion. (B) If both assertion and reason are true but reason is not the correct explanation of the assertion. (C) If assertion is true but reason is false. (D) If assertion and reason both are false. Assertion: Young's modulus for a perfectly plastic body is zero. Reason: For a perfectly plastic body restoring force is zero. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) d

Short Answer

Expert verified
The correct option is (A) because both the assertion and reason are true, and the reason correctly explains the assertion. Young's modulus for a perfectly plastic body is indeed zero, as there is no restoring force after deformation, which leads to no relationship between stress and strain.

Step by step solution

01

Understand the Young's modulus

Young's modulus (Y) is a measure of the stiffness of a material, quantifying the relationship between stress (force per unit area) and strain (deformation) for an elastic material. It is defined by the formula: \[ Y = \frac{stress}{strain} = \frac{F/A}{\Delta L/L} \] where: - Y is the Young's modulus - F is the force applied to the material - A is the cross-sectional area of the material - ΔL is the change in length of the material - L is the original length of the material Step 2: Understand the behavior of a perfectly plastic body
02

Understand the behavior of a perfectly plastic body

A perfectly plastic body is a hypothetical material that undergoes permanent deformation under stress without requiring any additional force. In other words, once the yield strength is reached, the material deforms at a constant stress without increasing the force necessary to sustain this deformation. For a perfectly plastic body, there is no restoring force that allows the material to return to its original shape. Step 3: Evaluate the assertion
03

Evaluate the assertion

The assertion states that the Young's modulus for a perfectly plastic body is zero. This is true because the perfectly plastic body experiences no restoring force after deformation, and therefore there is no relationship between stress and strain, resulting in a Young's modulus of zero. Step 4: Evaluate the reason
04

Evaluate the reason

The reason states that for a perfectly plastic body, the restoring force is zero. This is also true, as we have previously described the behavior of a perfectly plastic body and established that it has no restoring force, allowing it to return to its original shape after deformation. Step 5: Choose the correct option
05

Choose the correct option

Since both the assertion and reason are true and the reason explains the assertion (the restoring force being zero is the cause of the Young's modulus being zero), the correct option is (A).

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