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The bar shown in the figure is made of a...

The bar shown in the figure is made of a single piece of material. It is fixed at one end. It consists of two segments of equal lengh `L//2` each but different cross sectional area `A` and `2A`. Find the ratio of total elongation in the bar to the elongation produced in thicker segment under the action of an axial force `F`. Consider the shape of the joint to remain circular. (Given :`Y` is Young's modulus.

Text Solution

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The correct Answer is:
3
`/_\L=(F(L//2))/(AY)=(FL)/(2AY)`
`=/_\L_2=(F(L//2))/(2AY)=(FL)/(4AY)`
Required ratio `=(/_\L_1+/_\L_2)/(/_\L_2)=(/_\L_1)/(/_\L_2)+1=2+1=3`
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