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Q.
A rope $1 \,cm$ in diameter breaks if tension in it exceeds $500\, N$. The maximum tension that may be given to a similar rope of diameter $2 \,cm$ is
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 $\frac{500}{(1 \,cm )^{2}}=\frac{T_{2}}{(2\, cm )^{2}}$
or $\,\,\, T_{2}=4 \times 500=2000 N$