Question

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by ΔT. The net change in its length is zero. Let L be the length of the rod, A is its area of cross-section. Y is Young’s modulus, and α is its coefficient of linear expansion. Then, F is equal to

• A. (A) L2YaΔT
• B. (B) AYaΔT
• C. (C) AYaΔT
• D. (D) LAYaΔT

Answer 1

Answer: (C)

(C) AYaΔT

Answer 2

Explanation:
Thermal expansion, ΔL=LaΔT.....(i)Compression ΔL′ produced by applied force is given by,Y=FLAΔL′⇒F=YAΔL′L......(ii)Net change in length =0⇒ΔL′=ΔL......(iii)From equation (i),(ii) and (iii) we get,F=YA×(LaΔT)L=YAaΔTHence, the correct option is (C).