A steel rod of length 1 m and cross sectional area 10-4 m² is heated from 0°C to 200°C without being allowed to extend or bend. The compressive tension produced in the rod is______ ×104N. (Given Young's modulus of steel = 2×1011 Nm-2, coefficient of linear expansion = 10-5K-1)
To find the compressive tension produced in the steel rod, we begin by understanding that due to heating, the rod tends to expand. However, since it is not allowed to extend, compressive stress is introduced to counteract the expansion.
The formula for the force due to thermal expansion when the length is constrained is:
F = Y × A × α × ΔT
Where:
Y is Young's modulus (2×1011 Nm-2)
A is the cross-sectional area (10-4 m2)
α is the coefficient of linear expansion (10-5 K-1)
ΔT is the change in temperature (200°C - 0°C = 200 K)
Substituting the known values:
F = (2×1011) × (10-4) × (10-5) × 200
Simplifying:
F = 2 × 102 × 2
F = 4 × 102N = 400 N
The compressive tension produced, expressed as × 104N, is:
F = 0.04 × 104N
Verifying within the given range (4,4):
0.04 × 104 N corresponds to a formulaic answer of 4.
Thus, the compressive tension produced in the rod is 4 × 104 N.
