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  • A metal wire of length and cross-sectional area <img alt="10^{-4} \mathrm{~m}^{2}" src=

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 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}

Option: 1

50


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{\ell=0.5m}

\mathrm{A=10^{-4}m^{2}}

\mathrm{Stress=5\times 10^{8}}

\mathrm{T =\frac{m v^2}{\ell} }

\mathrm{\text { Stress } =\frac{I}{A}=\frac{m v^2}{\ell A} }

\mathrm{5 \times 10^8 =\frac{10 v^2}{(0.5) \times 10^{-4}} }

\mathrm{2.5 \times 10^3 =V^2 }

\mathrm{V^2 =2500 }

\mathrm{V =50 \mathrm{~m} / \mathrm{s} }

The maximum linear velocity will be \mathrm{50 \mathrm{~m} / \mathrm{s} }

Posted by

Sanket Gandhi

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