A metal wire of length $0.5 m$ and cross-sectional area $10^{-4}\; m ^{2}$ has breaking stress $5 \times 10^{8}\; Nm ^{-2}$. A block of $10\; kg$ is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be $ms ^{-1}$.
JEE MAIN 2022, Diffcult
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$T =\frac{ mv ^{2}}{\ell}=\frac{10 \times v ^{2}}{0.5}=20\,v ^{2}$
$T _{\max }=$ Breaking stress $\times$ Area
$=5 \times 10^{8} \times 10^{-4}=5 \times 10^{4}$
$20\,V ^{2}=5 \times 10^{4}$
$V=\sqrt{\frac{1}{4} 10^{4}}=50\,m / s$
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