Question

A steel wire of length \( L \) and area of cross-section \( A \) is suspended from rigid support. If \( Y \) is the Young's modulus of material of the wire and \( \alpha \) is the coefficient of linear expansion, then the increase in tension when temperature falls by \( t^\circ C \) is

• A. \( \frac{YA}{\alpha t} \)
• B. \( YA \alpha t \)
• C. \( YA t \)
• D. \( \frac{LA \alpha t}{Y} \)

Hint:

In problems involving thermal expansion and tension, the change in tension is proportional to Young's modulus, the area of cross-section, the coefficient of linear expansion, and the temperature change.

Answer 1

The Correct Option is B

Step 1: Understanding the relationship for tension.
The change in tension in the wire due to a change in temperature is given by: \[ \Delta T = YA \alpha t \] Where: - \( Y \) is the Young's modulus of the wire, - \( A \) is the area of cross-section, - \( \alpha \) is the coefficient of linear expansion, - \( t \) is the change in temperature. Thus, the correct answer is (B) \( YA \alpha t \).