Metal length cross-sectional |ELASTICITYVISCOSITYJEEMain2022

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JEE MAIN 2022

29-07-2022 S2

Question

A metal wire of length 0.5 m and cross-sectional area $10^{-4} \mathrm{~m}^2$ has breaking stress $5 \times 10^8 \mathrm{Nm}^{-2}$. 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 ______$\mathrm{ms}^{-1}$.

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$\begin{aligned} & \mathrm{T}=\frac{\mathrm{mv}^2}{\ell}=\frac{10 \times \mathrm{v}^2}{0.5}=20 \mathrm{v}^2 \\ & \mathrm{~T}_{\max }=\text { Breaking stress } \text { × } \text { Area } \\ & =5 \times 10^8 \times 10^{-4}=5 \times 10^4 \\ & 20 \mathrm{~V}^2=5 \times 10^4 \\ & \mathrm{~V}=\sqrt{\frac{1}{4} 10^4}=50 \mathrm{~m} / \mathrm{s}\end{aligned}$

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