A force of 500N1 is applied to a steel wire of cross-sectional area 0.2m2, The tensile stress is

Analysis

To solve this problem, we need to calculate the tensile stress acting on the steel wire. Stress is defined as the force applied per unit cross-sectional area of a material.

Concept

The formula for tensile stress ($\sigma$) is:

• Force ($F$): Measured in Newtons (N).
• Area ($A$): Measured in square meters ($m^2$).
• Unit of Stress: The SI unit is Newtons per square meter ($Nm^{-2}$) or Pascals (Pa).

Solution

Given the values from your question:

• Force ($F$) = $500 \, \text{N}$
• Area ($A$) = $0.2 \, \text{m}^2$

Substitute these values into the formula:

To simplify the division, you can multiply both the numerator and the denominator by 10 to remove the decimal:

Now, express $2500$ in standard form:

The calculated value is $2.5 \times 10^3 \, \text{Nm}^{-2}$, which matches option D.

Exam Tip

When dealing with stress and pressure problems, always ensure your area is in square meters ($m^2$). If the question gives you the area in $cm^2$ or $mm^2$, you must convert it to $m^2$ first (e.g., $1 \, \text{cm}^2 = 10^{-4} \, \text{m}^2$) before dividing, otherwise, your answer will be incorrect!