A thin rod of negligible mass and area of cross-section 4 × 10 - 6 m 2 , suspended vertically from one end, has a length of 0.5 m at 100 ° C . The rod is cooled to 0 ° C but prevented from contracting by attaching a mass at the lower end. The value of this mass is (Given, coefficient of linear expansion is 10 - 5 ° C - 1 , Young's modulus is Y = 10 11 N m - 2 and g = 10 m s - 2 )

Step-by-step solution

The change in length due to decrease in temperature, Δ l 1 = L α Δ θ = 0 · 5 10 - 5 0 - 100 Δ l 1 = - 0 · 5 × 10 - 3   m ... (i) Negative sign implies that length is decreasing. Now let M be the mass attached to the lower end. Then, change in length due to suspension of load is Δ l 2 = Mg L AY = M 10 0.5 4 × 10 - 6 10 11 Δ l 2 = 1.25 × 10 - 5 M ... (ii) Δ l 1 + Δ l 2 = 0 ⇒ 1.25 × 10 - 5 M = 0.5 × 10 - 3 (from equations (i) an