Question

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 __ $ms ^{-1}$.

Answer 1

$ T =\frac{ mv ^2}{\ell}=\frac{10 \times v ^2}{0.5}=20 v ^2 $
$ T _{\max }=\text { Breaking stress } \times \text { 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$