Coefficient of linear expansion of brass and steel rods are ₁ and ₂ . Lengths of brass and steel rod are l₁ and l₂ respectively. Though the temperature of brass and steel is increased, (l₂ - l₁) is maintained same at all temperatures, which of the following relations holds good?

Step-by-step solution

Let the initial lengths of the brass and steel rods be l₁ and l₂ respectively at temperature T . When the temperature is increased by T , the new lengths are: l₁' = l₁(1 + ₁ T) l₂' = l₂(1 + ₂ T) The difference in lengths at the new temperature is: l₂' - l₁' = l₂(1 + ₂ T) - l₁(1 + ₁ T) l₂' - l₁' = (l₂ - l₁) + (l₂ ₂ - l₁ ₁) T Given that the difference in lengths (l₂ - l₁) is maintained the same at all temperatures, we have: l₂' - l₁' = l₂ - l₁ Substituting this into the equation gives: (l₂ ₂ - l₁ ₁) T = 0 Since T 0 ,