Question

Two wires A and B are stretched by the same load. The radius of wire A is double the radius of wire B. The stress on the wire B as compared to the stress on the wire A is

• A. twice.
• B. four times.
• C. half.
• D. equal.

Hint:

Stress is inversely proportional to the cross-sectional area of the wire, so when the radius doubles, the stress increases by a factor of four.

Answer 1

The Correct Option is B

Step 1: Understanding stress and its relation.
Stress is defined as force per unit area, \( \sigma = \frac{F}{A} \), where \( F \) is the force applied and \( A \) is the cross-sectional area of the wire. Since wire A has twice the radius of wire B, the area of wire A is four times greater than that of wire B (because area \( A = \pi r^2 \)).
Step 2: Relating stress to the radius.
Since stress \( \sigma \) is inversely proportional to the cross-sectional area \( A \), the stress on wire B will be four times that on wire A, given that wire A has a larger area.
Step 3: Conclusion.
The stress on wire B is four times greater than on wire A, hence the correct answer is (B) four times.