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 ${10}^{-3}m$.Find the Young's modulus of the wire (in terms of ${10}^{11}N/m^2$)

Answer 1

The force in the string due to the rotating motion is $F=m{\omega }^{2}l=1\times (20{)}^2\times 1=400N$
The Young's modulus is $Y=\frac{Fl}{A\Delta l}=\frac{400\times 1}{{10}^{-6}\times {10}^{-3}}=4\times {10}^{11}N/m^2$