A thin uniform copper rod of length l and cross-section area A and mass m rotates uniformly with an angular velocity `omega` in a horizontal plane about a vertical axis passing through one of its ends. The elongation of the rod will be

Options

A. `(momega^(2)l^(2))/(6AY)`
B. `(momega^(2)l^(2))/(3AY)`
C. `(momega^(2)l^(2))/(AY)`
D. `(momega^(2)l^(2))/(2AY)`

Answer

C

Explanation

Free expansion of rod = `alphaLDeltatheta=15 xx 10^(-6)xx2(50-20)=15xx10^(-6)xx2xx30=0.9mm`
If expansion is fully prevented Strain = `(DeltaL)/(L)=(9xx10^(-4))/(2)=4.5 xx10^(-4)`
Thermal stress = (strain)Y = `(4.5 xx 10^(-4))(2xx10^(11))=9xx10^(7)N//m^(2)`