Question

A thick metal wire of density \( \rho \) and length \( L \) is hung from a rigid support. The increase in length of the wire due to its own weight

• A. \( \frac{\rho L^2 g}{2 Y} \)
• B. \( \frac{g \rho L^2}{2 Y} \)
• C. \( \frac{\rho g L^2}{2 Y} \)
• D. \( \frac{\rho g L^2}{4 Y} \)

Answer 1

The Correct Option is B

The increase in length due to the weight of the wire can be calculated using the formula for elongation under tension:
\( \Delta L = \frac{F L}{A Y} \), where \( F = \rho g L^2 \) is the force due to the weight, and \( Y \) is the Young's modulus.