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Question
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
Options
500 N
250 N
1000 N
2000 N
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Solution
\[F_1 = 500\text{N}\]
\[\text{ Let the required breaking force on the 2 cm wire be F .} \]
\[\text{ Breaking stress in 1 cm wire }= \frac{F_1}{A_1} = \frac{500}{\pi \left( \frac{0 . 01}{2} \right)^2}\]
\[\text{ Breaking stress in 2 cm wire }= \frac{F_2}{A_2} = \frac{F_2}{\pi \left( \frac{0 . 02}{2} \right)^2}\]
\[\text{ The breaking stress is the same for a material }. \]
\[ \Rightarrow \frac{500}{\pi \left( \frac{0 . 01}{2} \right)^2} = \frac{F_2}{\pi \left( \frac{0 . 02}{2} \right)^2}\]
\[ = > F_2 = 2000\text{N}\]
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