A metal rod A of 25cm lengths expands by 0.050 cm, when its temperature is raised from 0°C to 100°C. Another rod B of a different metal of length 40cm expands by 0.040 cm for the same rise in temperature. A third rod C of 50cm length is made up of pieces of rods A and B placed end to end expands by 0.03cm on heating from 0°C to 50°C. Find the lengths of each portion of the composite rod. Which of the following gives the correct final result?
Options

Question

A metal rod A of 25cm lengths expands by 0.050 cm, when its temperature is raised from 0°C to 100°C. Another rod B of a different metal of length 40cm expands by 0.040 cm for the same rise in temperature. A third rod C of 50cm length is made up of pieces of rods A and B placed end to end expands by 0.03cm on heating from 0°C to 50°C. Find the lengths of each portion of the composite rod. Which of the following gives the correct final result?

Options

G1 Physics · Accepted Answer

Use ΔL=αLΔT, ΔA≈2αAΔT and ΔV≈3αVΔT (or the given cubical coefficient γ). For constrained bodies include the elastic stress needed to cancel free expansion. Evaluating the given data/statements gives 10 cm; 40 cm. Therefore the correct answer is A.