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A uniform elastic plank moves due to a constant force F placed over a smooth 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?

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$\frac{F}{2 S E}$

zero

$\frac{F}{4 S E}$

$\frac{F}{S E}$

answer is B.

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Detailed Solution

Tension at distance x from end $A, T_{x} = F - \frac{F}{L} x$

Total change in length, $Δ L = \int_{0}^{L} \frac{T_{x} d x}{E S} = \frac{F L}{2 E S}$

$∴$ Average strain $= \frac{Δ L}{L} = \frac{F}{2 E S}$

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