A rope 1 cm in diameter breaks if the tension in it exceeds 500 N. The maximum tension that may be given to a similar rope of diameter 2 cm is

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KollegeApply · Accepted Answer

F_1 = 500\text{N} \text{ Let the required breaking force on the 2 cm wire be F .} \text{ Breaking stress in 1 cm wire }= F_1/A_1 = \frac{500}{$\pi$ \left( 0 . $\frac{01}{2}$ \right)^2} \text{ Breaking stress in 2 cm wire }= F_2/A_2 = \frac{F_2}{$\pi$ \left( 0 . $\frac{02}{2}$ \right)^2} \text{ The breaking stress is the same for a material }. \Rightarrow \frac{500}{$\pi$ \left( 0 . $\frac{01}{2}$ \right)^2} = \frac{F_2}{$\pi$ \left( 0 . $\frac{02}{2}$ \right)^2} = > F_2 = 2000\text{N}

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