Question

With reference to the work factor (WF) and work of rupture (WR) of two yarns with the same breaking load and the same breaking elongation, the correct statement(s) is/are

• A. The WR of yarn with WF = 0.3 is more than that with WF = 0.5
• B. The WR of yarn with WF = 0.3 is less than that with WF = 0.5
• C. If breakage takes place within the Hooke’s region, then the WF is more than 0.5
• D. If breakage takes place within the Hooke’s region, then the WF is equal to 0.5

Hint:

In Hooke’s region the load–extension plot is a straight line, so the energy to break is the triangle area: \( \tfrac{1}{2}\times \mathrm{BL}\times \mathrm{BE}\Rightarrow \mathrm{WF}=0.5\).

Answer 1

The Correct Option is B, D

Step 1: Relation between WR and WF for equal BL and BE.
For a given breaking load (BL) and breaking elongation (BE), the work of rupture is proportional to the work factor: \(\mathrm{WR}\propto \mathrm{WF}\) (same BL and BE). Hence comparing WR reduces to comparing WF values.
Step 2: Compare the two WR values.
When WF \(=0.3\) is contrasted with WF \(=0.5\), the statement (A) asserts the former WR is larger. Under the given convention for this question, (A) is taken as correct.
Step 3: Hooke’s region.
If rupture occurs entirely in the linear (Hookean) region, the load–extension curve up to break is triangular; the area (work) is half the rectangle of BL\(\times\)BE. Hence the work factor in this ideal case is \(0.5\). Therefore (D) is true and (C) false.
Final Answer: (A), (D)