Question

A copper wire of negligible mass, $1m$ length and cross-sectional area ${10}^{-6}{m}^2$ is kept on a smooth horizontal table with one end fixed. A ball of mass $1kg$ is attached to the other end. The wire and the ball are rotating with an angular velocity of $20rad/s$. If the elongation in the wire is ${10}^{-3}m$. If for the same wire as stated above, the angular velocity is increased to $100rad/s$ and the wire breaks down, find the breaking stress (in terms of ${10}^{10}N/m^2$).

Answer 1

Breaking stress $=\frac{F}{A}=\frac{m{\omega }^{2}l}{A}=\frac{1\times {100}^2\times 1}{{10}^{-6}}={10}^{10}N/m^2$