A steel rod of length 25 cm has a cross-sectional area of 0.8 cm 2. The force (in N ) required to stretch this rod by the same amount as the expansion produced by heating it through 10° C is coefficient of linear expansion of steel is 10-5 ° C -1. Young's modulus of steel is 2 × 1010 N / m 2.

Question

A steel rod of length 25 cm has a cross-sectional area of 0.8 cm 2. The force (in N ) required to stretch this rod by the same amount as the expansion produced by heating it through 10° C is coefficient of linear expansion of steel is 10-5 ° C -1. Young's modulus of steel is 2 × 1010 N / m 2. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

F = YA (Δ L / L )= YA α Δ T =2 × 1010 ×(0.8 × 10-4) × 10-5 × 10 N =160 N

Q. A steel rod of length 25cm has a cross-sectional area of 0.8cm2. The force (in N ) required to stretch this rod by the same amount as the expansion produced by heating it through 10∘C is coefficient of linear expansion of steel is 10−5∘C−1. Young's modulus of steel is 2×1010N/m2.

F=YALΔL​=YAαΔT =2×1010×(0.8×10−4)×10−5×10N =160N

$F = Y A \frac{Δ L}{L} = Y A α Δ T$
$= 2 \times 1 0^{10} \times (0.8 \times 1 0^{- 4}) \times 1 0^{- 5} \times 10 N$
$= 160 N$