There is some change W length when a 33000 N tensile force is applied on a steel rod of area of cross-section 10-3 m2. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is 3 × 1011 N/m2 and the coefficient of linear expansion of steel is 1.1 × 10-5 /° C).

Question

There is some change W length when a 33000 N tensile force is applied on a steel rod of area of cross-section 10-3 m2. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is 3 × 1011 N/m2 and the coefficient of linear expansion of steel is 1.1 × 10-5 /° C). (A) 20° C  (B) 15° C  (C) 10° C  (D) 0° C

Tardigrade Admin · Accepted Answer

Modulus of elasticity =( text Force / text Area ) × (l/Δ l) 3 × 1011=(33000/10-3) × (l/Δ l) (Δ l/l)=(33000/10-3) × (1/3 × 1011) =11 × 10-5 Change in length, (Δ l/l)=α Δ T 11 × 10-5=1.1 × 10-5 × Δ T ⇒ Δ T=10 K or 10° C

$2 0^{\circ} C$

$1 5^{\circ} C$

$1 0^{\circ} C$

$0^{\circ} C$

20∘C

15∘C

10∘C

0∘C

Modulus of elasticity = Area Force ​×Δll​ 3×1011=10−333000​×Δll​ lΔl​=10−333000​×3×10111​ =11×10−5 Change in length, lΔl​=αΔT 11×10−5=1.1×10−5×ΔT ⇒ΔT=10K or 10∘C

$2 0^{\circ} C$

$1 5^{\circ} C$

$1 0^{\circ} C$

$0^{\circ} C$