The thermal stress developed in the steel rod is 4680 N/cm², which is approximately equal to 3) 3.6 MPa. Therefore , 3) 3.6 MPa is correct .
The thermal stress developed in the steel rod can be calculated using the following formula:
σ = EαΔT
where:
σ is the thermal stress (N/m²)
E is the Young's modulus of steel (200 GPa)
α is the coefficient of thermal expansion of steel (11.7 × 10⁻⁶ m/°C)
ΔT is the change in temperature (°C)
In this case, the dimensions of the steel rod are 4 cm × 4 cm, which is equal to 0.04 m × 0.04 m.
The change in temperature is 2°C. Plugging these values into the formula, we get:
σ = (200 × 10⁹ N/m²) × (11.7 × 10⁻⁶ m/°C) × (2°C) = 46800000 N/m²
Converting this to N/cm², we get:
σ = 46800000 N/m² ÷ 10000 cm²/m² = 4680 N/cm²
Therefore, the thermal stress developed in the steel rod is 4680 N/cm², which is approximately equal to 3.6 MPa.
Question
A steel rod of dimensions 4 x 4cm is tightly fixed between two supports and is not allowed to expand. It is heated through 2°C. Thermal stress developed is ..... 10 N/m² (Y= 20 x101°N/m a = 18 x 10-6/°C)
1) 7.2
2) 2.7
3) 3.6
4) 0.72