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  4. A body of mass m=10 kg is attached to one end of a wire of length 0.3 m . What is the maximum angular speed (in rad s- 1 ) with which it can be rotated about its other end in a space station without breaking the wire? [Breaking stress of wire =4.8× 107 N m- 2 and area of cross-section of the wire =10- 2 cm2 ]

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Q. A body of mass $m=10 \, kg$ is attached to one end of a wire of length $0.3 \, m$ . What is the maximum angular speed (in $rad \, s^{- 1}$ ) with which it can be rotated about its other end in a space station without breaking the wire?

[Breaking stress of wire $=4.8\times 10^{7} \, N \, m^{- 2}$ and area of cross-section of the wire $=10^{- 2} \, cm^{2}$ ]

NTA AbhyasNTA Abhyas 2020

Solution:

Solution
$\frac{T}{A}=\sigma \ldots \ldots \ldots \ldots \ldots \ldots \ldots .\left(1\right)$
$T=\left(mω\right)^{2}l\ldots \ldots \ldots \ldots \ldots \ldots \ldots .\left(2\right)$
Solving we get,
$\omega =4rads^{- 1}$