A string A of length 0.314 m and Young's modulus 2 10¹⁰ N/m ^2 is connected to another string B of length and Young's modulus both twice of those of A . This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is _____ mm. (radius of both the strings is 0.2 mm and acceleration due to gravity = 10 m/s ^2 )

Step-by-step solution

Given: Length of string A, L_A = 0.314 m Young's modulus of string A, Y_A = 2 10¹⁰ N/m ^2 Radius of both strings, r = 0.2 mm = 2 10⁻⁴ m Length of string B, L_B = 2L_A = 0.628 m Young's modulus of string B, Y_B = 2Y_A = 4 10¹⁰ N/m ^2 Mass of load, m = 0.8 kg Acceleration due to gravity, g = 10 m/s ^2 Tension in both strings, T = mg = 0.8 10 = 8 N Cross-sectional area of both strings: A = r^2 = 3.14 (2 10⁻⁴)^2 = 3.14 4 10⁻⁸ m ^2 Elongation in string A: L_A = T L_A A Y_A L_A = 8 0.314 3.14 4 10⁻⁸ 2 10¹⁰ L_A = 8 0.314