A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of 0.2 mm between the rod and the wall on the right side. If the temperature of the rod is increased by 200∘c, then the axial stress developed in the rod is
Free expansion of rod = LαΔT
=250×10−5×200=0.5mm
Actual expansion = 0.2 mm
∴ Expansion resisted = 0.3 mm
∴ Strain resisted =0.3250
∴ Strees developed =0.3250×200×103
=0.24×103=240 MPa