A metal wire of length $0.5 \mathrm{~m}$ and cross-sectional area $10^{-4} \mathrm{~m}^{2}$ has breaking stress $5 \times 10^{8} \,\mathrm{Nm}^{-2}$. A block of $10 \mathrm{~kg}$ is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _________ $\mathrm{ms}^{-1}$.
Answer (integer)
50
Solution
$\mathrm{T}=\frac{\mathrm{mv}^2}{\ell}=\frac{10 \times \mathrm{v}^2}{0.5}=20 \mathrm{v}^2$
<br/><br/>$\mathrm{~T}_{\max }=$ Breaking stress $\times$ Area
<br/><br/>$=5 \times 10^8 \times 10^{-4}=5 \times 10^4$
<br/><br/>$20 \mathrm{~V}^2=5 \times 10^4$
<br/><br/>$\mathrm{~V}=\sqrt{\frac{1}{4} \times 10^4}=50 \mathrm{~m} / \mathrm{s}$
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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