Question

A steel rail of length 5 m and area of cross-section 40 cm2 is
prevented from expanding along its length while the
temperature rises by 10°C. If coefficient of linear expansion
and Young's modulus of steel are 1.2 x 10-5 K-1 and 2 x 1011
Nm-2 respectively, the force developed in the rail is
approximately
100
(a) 2x10^7N (b) 1 x 10^5N
(c) 2x 10^9N
(d) 3 x 10^-5 N​

Answer 1

answer : option (b) 10^5 N

Young's modulus, Y = Fl/A∆l

from thermal expansion, ∆l = lα∆T

so, Young's modulus, Y = F/Aα∆T

⇒F = YAα∆T

here, A = 40 cm² = 40 × 10^-4 m²

α = 1.2 × 10^-5 /K

Y = 2 × 10¹¹ N/m²

and ∆T = 10°C = 10K [ change in temperature for both (Kelvin and Celsius) systems are same. ]

now, F = 2 × 10¹¹ × 40 × 10^-4 × 1.2 × 10^-5 × 10

= 96 × 10² × 10

≈ 10^5 N

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Answer 2

$\huge\bold\purple{Answer:-}$

(b) 1 x 10^5N