Question

The ultimate tensile strength of a material is 400 MPa. If the diameter of the wire is 10 mm, what is the maximum force that can be applied to the wire before it breaks?

• A. 3144 N
• B. 2827 N
• C. 314 N
• D. 282 N

Hint:

To calculate the maximum force, multiply the tensile strength by the cross-sectional area of the wire.

Answer 1

The Correct Option is A

The force is given by: \[ F = \sigma \times A \] where $\sigma$ is the ultimate tensile strength and $A$ is the cross-sectional area. The area of a circular cross-section is: \[ A = \pi \left(\frac{d}{2}\right)^2 = \pi \left(\frac{10}{2}\right)^2 = 78.54 \, \text{mm}^2 \] The force is: \[ F = 400 \times 78.54 = 3144 \, \text{N} \]