The bar shown in the figure is made of a single piece of material. It is fixed at one end and consists of two segments of equal length 2 L but different cross-sectional area A and 2A. What is the change in length of the entire system under the action of an axial force F ? [Consider the shape of joint to remain circular, Y is young's modulus].
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Question

The bar shown in the figure is made of a single piece of material. It is fixed at one end and consists of two segments of equal length 2 L but different cross-sectional area A and 2A. What is the change in length of the entire system under the action of an axial force F ? [Consider the shape of joint to remain circular, Y is young's modulus].

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G1 Physics · Accepted Answer

Use stress σ=F/A, strain ε=ΔL/L and Young's modulus Y=σ/ε. For a uniform segment, ΔL=FL/(AY); for thermal restraint, thermal strain αΔT produces stress YαΔT. Evaluating the given data/statements gives A: 3FL/(4AY). Therefore the correct answer is A.