Question

A wire is replaced by another wire of the same length and material but twice the diameter. The maximum load, which the second wire can bear, will:

• A. remain the same
• B. decrease to four times
• C. increase to four times
• D. increase to a factor of 2

Answer 1

The correct option is C increase to four times

$\begin{array}{c}Y=\frac{F}{A}\frac{AL}{\Delta L}\\ \text{load}F=\frac{YA\Delta L}{L}=D^2\left(\frac{M\pi \Delta }{4}L\right)\end{array}$

$\begin{array}{cc}\mathrm{load}F& \alpha D^2\\ D^{\prime }& =2D\\ F^{\prime }& =4F\end{array}$

$\text{Therefore maximum load increases to feur times.}$