Q: A steel wire AB of length 100 cm is fixed rigidly at points A and B in an aluminium frame as shown in the figure. If the temperature of the system increases through 100°C, then the excess stress produced in the steel wire relative to the aluminium? aAl = 22× 10-6/°C and asteel = 11 × 10-6/°C young’s Modulus of steel is 2×1011 Nm-2.
(a) 2.2 × 108 Pa
(b) 22 × 108 Pa
(c) 0.2 × 108 Pa
(d) 220 × 108 Pa
Ans: (a)
Sol: As αa > αs , on heating, aluminium frame will expand more than the steel wire .
Thermal strain in steel wire relative to aluminium wire = (αa – αs)Δθ
= (22 – 11) × 10-6 × [110 – 10]
= 1.1 × 10-3
Thermal stress = Y × Thermal strain
= 2 × 1011 × 1.1 × 10-3
= 2.2 × 108 N/m2