Two blocks of masses $3 \,{kg}$ and $5\, {kg}$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi} \times 10^{2}\, {Nm}^{-2}$. What is the minimum radius of the wire? (Take $\left.g=10\, {ms}^{-2}\right)$ (in $cm$)
JEE MAIN 2021, Diffcult
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${T}=\frac{2 {m}_{1} {m}_{2} {g}}{{m}_{1}+{m}_{2}}=\frac{2 \times 3 \times 5 \times 10}{8}$
$=\frac{75}{2}$
Stress $=\frac{{T}}{{A}}$
$\frac{24}{\pi} \times 10^{2}=\frac{75}{2 \times \pi {R}^{2}}$
${R}^{2}=\frac{75}{2 \times 24 \times 100}=\frac{3}{8 \times 24}$
$\Rightarrow {R}=0.125\, {m}$
${R}=12.5\, {cm}$
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