Question

Two rods one of aluminium and the other of steel; having initial lengths l₁ and l₂ at 0°C are connected together to form a single rod of length (l₁ + l₂). If the length of each rod increases by the same amount on increasing temperature by θ°C; the ratio l₁/(l₁+l₂) in terms of coefficents of linear expansions α₁ and α₂ is

(1) \(\frac{a_1}{a_2}\)

(2) \(\frac{a_2}{a_1}\)

(3) \(\frac{a_1}{a_1+a_2}\)

(4) \(\frac{a_2}{a_!+a_2}\)

Answer 1

 (4) \(\frac{a_2}{a_!+a_2}\)

The increase in length of the two rods on raising temperatior by θ°C is same. Therefore