Question

A polyester fibre rope of diameter $3cm$ has a breaking strength of $150kN$. If it is required to have $600kN$ breaking strength, what should be the diameter of similar rope?

• A. $12cm$
• B. $6cm$
• C. $3cm$
• D. $1.5cm$

Answer 1

Answer: (B)

$6cm$

$\begin{array}{c}\text{case}1\text{: Diameter}=3cm\text{, Breaking strength}=F_1=150kN\\ \frac{F_1}{A_1}=\frac{150kN}{{(\frac{3}{2}\times {10}^{-2})}^2}\end{array}$

$\text{case}2\text{: Let diameter be}dcm,F_2=600kN$

$\frac{150kN}{{(\frac{3}{2}\times {10}^{-2})}^2}=\frac{600kN}{{(\frac{d}{2}\times {10}^{-2})}^2}$

$\begin{array}{c}\Rightarrow \frac{1}{9}=\frac{4}{d^2}\\ \Rightarrow d^2=36\\ \Rightarrow d=6cm\text{Ans.}\end{array}$