Question

A body of mass $m=10kg$ is attached to one end of a wire of length $0.3m$ . 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 $=10^{-2}c{m}^2$ ]

Answer 1

Answer: 4

$\frac{T}{A}=\sigma \dots \dots \dots \dots \dots \dots \dots .\left(1\right)$
$T={\left(m\omega \right)}^{2}l\dots \dots \dots \dots \dots \dots \dots .\left(2\right)$
Solving we get,
$\omega =4rad{s}^{-1}$