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  • A uniform elastic plank moves due to a constant force F placed over surface. The area of end face is S and Young's modulus of the material is E. What is average strain produced in the direction

A uniform elastic plank moves due to a constant force F placed over surface. The area of end face is S and Young's modulus of the material is E. What is average strain produced in the direction of the force ?

Option: 1

\frac{F}{SE}


Option: 2

\frac{F}{2SE}


Option: 3

\frac{F}{4SE}


Option: 4

Zero


Answers (1)

best_answer

Tension at distance x from end A,

T_x=F-\frac{F}{L} \cdot x

\\Total\ change\ in\ length,\ \Delta l =\int_0^L \frac{T_x d x}{E S}\\ \Delta l=\frac{F L}{2 E S}\\ \begin{aligned} \therefore \text { Average strain } & =\frac{\Delta \ell}{L} \\ & =\frac{F}{2 E S} \end{aligned}

Posted by

vishal kumar

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