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A rope 1 cm in diameter breaks, if the t...

A rope 1 cm in diameter breaks, if the tension in it exceeds 500 N. The maximum tension that may be given to similar rope of diameter 3 cm is

A

2000 N

B

1000 N

C

500 N

D

250 N

Text Solution

Verified by Experts

The correct Answer is:
A
Breaking stress `= (F_(1))/(A_(1)) = (F_(2))/(A_(2))` or `(T_(1))/(A_(1)) = (T_(2))/(A_(2))`
`:. T_(2) = T_(1) ((A_(2))/(A_(1))) = T_(1)((pi r_(2)^(2))/(pi r_(1)^(2))) = T_(1)((r_(2))/(r_(1)))^(2)`
`:. T_(2) = 500 (2)^(2) = 2000 N`
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