Consider a brass rod and a steel rod ( 80 c m longer than the brass rod) at 0 ° C. It is observed that on increasing temperatures of the two rods by same amount difference in lengths of the two rods does not change. Given that the thermal coefficient of linear expansion for steel and brass are 11 × 10 - 6 ℃ - 1 and 19 × 10 - 6 ℃ - 1 respectively. The sum of lengths of the two rods at 0 o C is

Question

Consider a brass rod and a steel rod ( 80 c m longer than the brass rod) at 0 ° C. It is observed that on increasing temperatures of the two rods by same amount difference in lengths of the two rods does not change. Given that the thermal coefficient of linear expansion for steel and brass are 11 × 10 - 6 ℃ - 1 and 19 × 10 - 6 ℃ - 1 respectively. The sum of lengths of the two rods at 0 o C is, 2 m, 4 m, 3 m, 1.5 m

MARKS App · Accepted Answer

The length and coefficient of thermal expansion for the rods are respectively; λ 1 , α 1 → steel rod λ 2 , α 2 → Brass rod As difference in lengths is constant ⇒ Δ λ 1 = Δ λ 2 ⇒ λ 1 α 1 Δ T = λ 2 α 2 Δ T ⇒ λ 1 α 1 = λ 2 α 2 … . . i Also ⇒ λ 1 - λ 2 = λ … … i i λ 1 = 1 α 2 α 2 - α 1 and λ 2 = 1 α 1 α 2 - α 1 ⇒ sum = 1 α 2 + α 1 α 2 - α 1 = 80 × 30 8 = 300 c m = 3 m

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