The breaking stress of wire going over a smooth pully is $2 \times 10^9\, N/m^2$. What would be the minimum radius of wire used if it is not to break?
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$20-T=2 a$ $...(1)$
$\mathrm{T}-10=1 \mathrm{a}$ $...(2)$
$\Rightarrow \mathrm{T}=\frac{40}{3} \mathrm{N}$
Stress $=\frac{\mathrm{T}}{\mathrm{A}} \Rightarrow 2 \times 10^{9}=\frac{40 / 3}{\mathrm{A}}$
$A=\frac{20}{3} \times 10^{-9} \mathrm{m}^{2}$
$\pi r^{2}=\frac{20}{3} \times 10^{-9}$
$r=\left(\frac{20}{3} \times \frac{10^{-9}}{3.14}\right)^{1 / 2}=0.46 \times 10^{-4} \mathrm{m}$
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