Question

A cable is replaced by another one of same length and material, but twice the diameter. How does this affect the maximum load it can support without exceeding the elastic limit ?
(Mass of cable is negligible)

• A. Wire can support 8 times the original load
• B. Wire can support 16 times the original load
• C. Wire can support 6 times the original load
• D. Wire can support 4 times the original load

Answer 1

The correct option is D Wire can support 4 times the original load

Let ${\sigma }_m$ be the stress at the elastic limit, which is constant for a particular material.

$\therefore {\sigma }_m=\frac{M_{m}g}{\left(\pi D^2/4\right)}$

Where $M_m$ is the maximum load the wire can support.

$\Rightarrow M_m\propto D^2$

Clearly, if the diameter is doubled, the wire can support four times the original load.

Hence, option $\left(\text{D}\right)$ is correct.