Let a rope of mass M and length L and young's modulus of elasticity Y and cross-sectional area A is hung vertically. Calculate the increase in length. Which of the following gives the correct final result?
Options

Question

Let a rope of mass M and length L and young's modulus of elasticity Y and cross-sectional area A is hung vertically. Calculate the increase in length. Which of the following gives the correct final result?

Options

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 3MgL/(2AY). Therefore the correct answer is A.