Question

A metal wire of length $0.5m$ and cross-sectional area $10^{-4}{m}^2$ has breaking stress $5\times 10^{8}N{m}^{-2}$. A block of $10kg$ is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be __ $m{s}^{-1}$.

Answer 1

Answer: 50

$T=\frac{m{v}^2}{\ell }=\frac{10\times v^2}{0.5}=20v^2$
$T_{\max }=\text{ Breaking stress }\times \text{ Area }$
$=5\times 10^8\times 10^{-4}=5\times 10^4$
$20V^2=5\times 10^4$
$V=\sqrt{\frac{1}{4}10^4}=50m/s$