Hooke's Law and Elastic Limit in Rod Extension

Steps:

• Identify the linear portion of the e vs F graph, where extension is directly proportional to force.
• Calculate the gradient of this linear region to find the spring constant k, since e = (F/k) for Hooke's law.
• Note the point where the graph deviates from linearity, indicating the elastic limit.
• Beyond this, extension increases non-linearly due to plastic deformation.

Why C is correct:

• Option C correctly identifies the elastic region where stress is proportional to strain, per Hooke's law (stress = E × strain, with E as Young's modulus).

Why the others are wrong:

• A assumes proportionality throughout, ignoring plastic deformation after the elastic limit.
• B misapplies the graph by using total extension instead of strain for modulus calculation.
• D incorrectly extends Hooke's law beyond the yield point, where behavior is non-elastic.

Final answer: C