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Question: A steel cable with a radius 2 cm supports a chairlift at a ski area. If the maximum stress is not to...

A steel cable with a radius 2 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 N m−2,10^{8}\text{ N }\text{m}^{- 2}, the maximum load the cable can support is

A

4π×105 N4\pi \times 10^{5}\text{ N}

B

4π×104 N4\pi \times 10^{4}\text{ N}

C

2π×105 N2\pi \times 10^{5}\text{ N}

D

2π×104 N2\pi \times 10^{4}\text{ N}

Answer

4π×104 N4\pi \times 10^{4}\text{ N}

Explanation

Solution

: Here, r=2cm=2×10−2mr = 2cm = 2 \times 10^{- 2}m

Maximum load = Maximum stress × Area of cross-section

=108Nm−2×π×(2×10−2m)2= 10^{8}Nm^{- 2} \times \pi \times (2 \times 10^{- 2}m)^{2}

=4π×104N= 4\pi \times 10^{4}N