A rod of uniform cross section area A and length L has a weight W. It is suspended vertically from a fixed support. The material of the rod is homogeneous and the modulud of elasticity is Y. If a concentrated force F is also applied at the free end of the rod, then find the total elongation of the rod.

Dear Sanchit Gupta

Ans: First of all let's calculate the total extension of the rod.

We know that Stress/Strain =Υ. As the mass is uniformly distributed and hence it is acting at a distance L/2 from the top

so, W/A=ΥΔl/(L/2)

Hence Δl=WL/2AY;

now the external force F can act as both as a Tensile as well as compressive force.

hence the total change in length will be

case 1 Δl=(WL+F)L/2AY When F is tensile;

case 2Δl=(WL-F)L/2AY when F is compressive.

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