Question

A steel cable with a radius $2cm$ supports a chairlift at a ski area. If the maximum stress is not to exceed ${10}^{8}N{m}^{-2}$, the maximum load the cable can support is

• A. $4\pi \times {10}^{5}N$
• B. $4\pi \times {10}^{4}N$
• C. $2\pi \times {10}^{5}N$
• D. $2\pi \times {10}^{4}N$

Answer 1

The correct option is B $4\pi \times {10}^{4}N$

Here $r=2cm=2\times {10}^{-2}m$
Maximum load$=$ Maximum stress $\times$ Area of cross section
$={10}^{8}N{m}^{-2}\times \pi \times {(2\times {10}^{-2}{m}^{})}^2=4\pi {10}^{4}N$