A steel rod with a length of 2 m and a cross-sectional area of 4 cm ^2 shrinks by 0.1 cm as the temperature decreases during the night. Determine the tension developed in the rod during the night hours if it is clamped at both ends during the day. Young modulus of steel = 1.9 10¹¹ N/m ^2 .

Step-by-step solution

Given, length of the rod, L = 2 m Cross-sectional area, A = 4 cm ^2 = 4 10⁻⁴ m ^2 Change in length, L = 0.1 cm = 10⁻³ m Young's modulus, Y = 1.9 10¹¹ N/m ^2 The tension developed in the rod is given by the formula: F = Y A L L Substituting the given values: F = 1.9 10¹¹ 4 10⁻⁴ 10⁻³ 2 F = 1.9 2 10^4 F = 3.8 10^4 N = 38000 N