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?
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?
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To calculate the maximum force, multiply the tensile strength by the cross-sectional area of the wire.
Updated On: Jun 17, 2025
- 3144 N
- 2827 N
- 314 N
- 282 N
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The Correct Option is A
Solution and Explanation
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: \[ F = 400 \times 78.54 = 3144 \, \text{N} \]
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