An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30°C. The coefficient of linear expansion of aluminium and steel are 24× 10⁻⁶/°C and 1.2× 10⁻⁵/°C, respectively. The length of this composite rod when its temperature is raised to 100°C, is ____ cm.

Solution

Physics sir · 4 steps

Each rod is 60 cm long and stretches on its own; add the two stretches to get the new length.

1. Split the length. The rods have the same length, so each is 120/2 = 60 cm. The temperature rise is Δ T = 100 - 30 = 70 °C.

   Δ L = L α Δ T

2. Expand each rod. Aluminium: 60 × 24 × 10⁻⁶ × 70 = 0.1008 cm. Steel: 60 × 12 × 10⁻⁶ × 70 = 0.0504 cm.
3. Add them up. Total expansion is 0.1008 + 0.0504 = 0.1512 cm.
4. So. The new length is 120 + 0.1512 ≈ 120.15 cm, which is option (c).

The idea to keep. For rods joined end to end, each piece expands by its own LαΔ T, and the total change is just the sum. Use each rod's own length, not the combined length.

Answer from the NTA final answer key. Solution by PrepWiser.