Question

A rope $1cm$ 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

Answer: (A)

W e know that
Young's modulus, $Y=\frac{\text{ stress }}{\text{ strain }}$
$\Rightarrow Y=\frac{T}{A\times \text{ strain }}$
For same type of wire,
$(Y)($ strain $)=\frac{T}{A}\Rightarrow \frac{T_1}{A_1}=\frac{T_2}{A_2}$
where $T$ ’s are tensions in the wires and $A$' s are areas of cross-sections.
or $\frac{500}{\pi r_1^2}=\frac{T_2}{\pi r_2^2}$ or $\frac{500}{(1cm{)}^2}=\frac{T_2}{(2cm{)}^2}$
or $T_2=4\times 500=2000N$