Q. 26

# A steel rod of length 2l, cross sectional area A and mass M is set rotating in a horizontal plane about an axis passing through the centre. If Y is the Young’s modulus for steel, find the extension in the length of the rod. (Assume the rod is uniform.)

Force acting in this element due to rotating is

Where

df=force on that small element under consideration

dm=mass of element under consideration

ω=angular velocity (which will remain same for all particles)

x=distance from the axis of rotation

Now, Taking mass per unit length

We have taken 2L as we considering the length of half part to be L

Now we know a relation between young modulus and tension force, but since, force is a function of x hence we can only write the equation for a small element of length dx

Here we have represented extension in length as dr, since our original length is dx

Now we need to multiply it by 2 as we were considering only half length of rod,

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