A thin rod having a length of 1 m and area of cross-section 3 × 10 - 6 m 2 is suspended vertically from one end. The rod is cooled from 210 ° C to 160 ° C . After cooling, a mass M is attached at the lower end of the rod such that the length of rod again becomes 1 m . Young's modulus and coefficient of linear expansion of the rod are 2 × 10 11 N m - 2 and 2 × 10 - 5 K - 1 , respectively.

Step-by-step solution

Let Δ l be the decease in length of rod due to decease in temperature Then, Δ l = l α Δ T , here, coefficient of linear expansion is α = 2 × 10 - 5   K - 1 and Δ T = ( 483 - 433 )   K = 50   K Thus, Δ l = 1 × 2 × 10 - 5 × 50 = 10 - 3   m Young's modulus is stated as Y = F A Δ l l , here, F = M g . So, 2 × 10 11 = M g × 1 3 × 10 - 6 × 10 - 3 ⇒ M g = 2 × 10 11 × 3 × 10 - 9 = 6 × 10 - 2 Thu