Question

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

• A. $2000N$
• B. $1000N$
• C. $500N$
• D. $250N$

Answer 1

The correct option is A $2000N$

Young's modulus of the rope, $Y=\frac{Stress}{Strain}=\frac{T/A}{\Delta l/l}$

$⟹T=Y\times \frac{\Delta l}{l}\times \frac{\pi d^2}{4}$

where, $d$ is the diameter of the rope and $T$ is the tension

$\Rightarrow$$T\propto d^2$

$\Rightarrow \frac{T_2}{T_1}=\frac{d_2^2}{d_1^2}$

Given : $T_1=500$ N

$d_1=1$ cm

$d_2=2$ cm

$\Rightarrow \frac{T_2}{500}=\frac{2^2}{1^2}$

$\Rightarrow T_2=2000$ N