Question

The schematic of elastic recovery of a textile material is given below.

Where:
AB = original length; BD = total extension; CD = elastic extension; BC = permanent set.
With reference to the above schematic, consider the following statements:
P. For perfectly elastic material, BC = 0
Q. For perfectly elastic material, CD = 0
R. For perfectly plastic material, BC = 0
S. For perfectly plastic material, CD = 0
The combination of TRUE statements is:

• A. P and Q
• B. Q and R
• C. R and S
• D. P and S

Hint:

Perfectly elastic materials show zero permanent set (BC = 0). Perfectly plastic materials show zero elastic recovery (CD = 0). Understanding these behaviours helps in analysing stress–strain diagrams.

Answer 1

The Correct Option is D

Step 1: Understanding elastic and plastic behaviour.
A perfectly elastic material returns completely to its original length after the force is removed. Therefore, there is no permanent deformation. Hence, BC = 0 for a perfectly elastic material.
Step 2: Evaluating statements for elastic material.
P states BC = 0 for a perfectly elastic material — this is TRUE.
Q states CD = 0 for a perfectly elastic material — this is FALSE, because perfectly elastic materials store all deformation as elastic extension, so CD is maximum, not zero.
Step 3: Evaluating statements for plastic material.
A perfectly plastic material does not recover any extension after unloading. Therefore, no elastic extension exists, meaning CD = 0 is TRUE. Thus S is TRUE.
R states BC = 0 for perfectly plastic material — this is FALSE, because plastic materials have only permanent deformation, so BC is maximum, not zero.
Step 4: Conclusion.
The correct pair of true statements is P (elastic with no permanent set) and S (plastic with no elastic recovery). Therefore, the correct answer is option (D).