A must solve question of SOM to improve the basics of deformation

Hello readers,

Below is a question which we would recommend to solve from SOM for GATE and ESE Mains. Try it on your own first and then go through our solution.

ELONGATION AND MAXIMUM STRESS INDUCED  ON A ROTATING BAR

Find the maximum stress induced in the bar and the elongation due to rotation when
a) axis of rotation passes through centroid of the bar.
b) axis of rotation passes through one end of the bar.

Solution:

a)

Now let us come to the calculation of Maximum stress:

Expression for elongation and maximum stress in terms of density:

b)

Similar analysis can be done when the bar is rotating about one end to get the following expressions:

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