A uniform rod of length `l`, mass `m`, cross-sectional area `A` and Young's modulus `Y` is rotated in horizontal plane about a fixed vertical axis passing through one end, with a constant angular velocity `omega`. Find the total extension in the rod due to the tension produced in the rod.

Options

A. `(momega^2l^2)/(3AY)`
B. `(momega^3l^3)/(3AY)`
C. `(momega^2l^3)/(4AY)`
D. `(momega^3l^2)/(3AY)`

Answer

A

Explanation

`Y=((T)/((x)))/(((trianglee)/(trianglex)))`,`T(x)=(m)/(l)(1-x)omega^2((l-x)/(2)+x)`
`impliesT=(momega^2)/(2l)`,`de=(momega^2)/(2AYl)(1^2-x^2)dx`
`implies(momega^2)/(2AY)(l^3-(l^3)/(3))=(momega^2l^2)/(3AY)`
Extension `=(momega^2l^2)/(3AY)`