Interpreting stress-strain graph for material properties

Steps:

• Recall strain = extension / original length; same dimensions mean extension proportional to strain.
• For statement 1, compare strains of X and Y at same stress; if Y's strain is not twice X's, statement false.
• For statement 2, Young's modulus E = stress / strain; if P's E is twice Q's, P's strain is half Q's at same stress, confirming ratio.
• For statement 3, Hooke's law holds if graph is linear (straight line through origin) up to strain 0.1.

Why C is correct:

• C selects 2 and 3 only, as modulus ratio follows E = stress/strain definition, and initial linearity indicates Hooke's law compliance.

Why the others are wrong:

• A includes 1, but Y's extension is not twice X's, as strains differ non-linearly.
• B includes 1, which misinterprets strain comparison for same stress.
• D excludes 2, ignoring correct modulus ratio from inverse strain relationship.

Final answer: C