A steel rod (Y = 2.0 × 1011 Nm-2, and α = 10-5 °C-1) of length 1 m

1.	A steel rod (Y = 2.0 × 1011 Nm-2, and α = 10-5 °C-1) of length 1 m and area of crosssection 1 cm2 is heated from 0°C to 200°C without being allowed to extend or bend. What is the tension produced in the rod?
Answer» Here, the equation of thermal expansion for linear expansion will be applied because of increase in temperature of the rod, length, increase. ∆T = 200°C – 0°C = 200°C, α = 10^-5 °C^-1, l = 1 m Area of cross – section, A = 1 cm² = 1 × 10^-4m² ∴ \(\frac{∆l}{l}\) = α∆T = 10^-5 × 200 = 2 × 10^-3 Tension produced in steel rod = YAα∆T = 2.0 × 10¹¹ × 1 × 10^-4 × 2 × 10^-3 = 4 × 10⁴ N.

A steel rod (Y = 2.0 × 1011 Nm-2, and α = 10-5 °C-1) of length 1 m and area of crosssection 1 cm2 is heated from 0°C to 200°C without being allowed to extend or bend. What is the tension produced in the rod?

Answer»

Here, the equation of thermal expansion for linear expansion will be applied because of increase in temperature of the rod, length, increase.

∆T = 200°C – 0°C = 200°C, α = 10^-5 °C^-1, l = 1 m

Area of cross – section, A = 1 cm² = 1 × 10^-4m²

∴ \(\frac{∆l}{l}\) = α∆T = 10^-5 × 200 = 2 × 10^-3

Tension produced in steel rod = YAα∆T

= 2.0 × 10¹¹ × 1 × 10^-4 × 2 × 10^-3 = 4 × 10⁴ N.