Question

A steel wire can support a maximum load of W before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit

• A. W
• B. $\frac{W}{2}$
• C. $\frac{W}{4}$
• D. 4W

Answer 1

Answer: (C)

$\frac{W}{4}$

Answer 2

: Breaking Force = Breaking stress × Area of cross-section

For a given material of the wire, breaking stress is constant.

$\therefore\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}$

$F_{2} = F_{1}\left( \frac{A_{2}}{A_{1}} \right) = F_{1}\left( \frac{A_{1}/4}{A_{1}} \right) = \frac{F_{1}}{4} = \frac{W}{4}$