A copper wire of negligible mass, `1 m` length and cross-sectional area `10^(-6) m^(2)` is kept on a smooth horizontal table with one end fixed. A ball of mass `1 kg` is attached to the other end. The wire and the ball are rotating with an angular velocity of `20 rad//s`. If the elongation in the wire is `10^(-3) m`.
a. Find the Young's modulus of the wire (in terms of `xx 10^(11) N//m^(2)`).
b. If for the same wire as stated above, the angular velocity is increased to `100 rad//s` and the wire breaks down, find the breaking stress (in terms of `xx 10^(10) N//m^(2)`).

Explanation

`:.` Centripetal frce `F=n omega^(2)r`
`:.` Stress in the wire `=F/A=(m omega^(2)r)/A` and Strain in the wire `=(Delta l)/l`
Young's modulus Y
`=("Stress")/("Strain")=(m omega^(2) l.l)/(A. Deltal)=(1xx(20)^(2)xx(1)^(2))/(10^(-6)xx10^(-3))=4xx10^(11)N//m^(2)`.