A light rigid bar AB is suspended horizontally from two vertical wires, one of steel and one of brass, as shown in figure. Each wire is 2.00 m long. The diameter of the steel wire is 0.60 mm and the length of the bar AB is 0.20 m. When a mass of 10 kg is suspended from the centre of AB bar remains horizontal. (i) What is the tension in each wire? (ii) Calculate the extension of the steel wire and the energy stored in it. (iii) Calculate the diameter of the brass wire. (iv) If the brass wire were replaced by another brass wire of diameter 1 mm, where should the mass be suspended so that AB would remain horizontal? The Young modulus for steel = 2.0 ×10¹¹ Pa, the Young modulus for brass = 1.0 ×10¹¹ Pa. Which of the following gives the correct final result?
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Question

A light rigid bar AB is suspended horizontally from two vertical wires, one of steel and one of brass, as shown in figure. Each wire is 2.00 m long. The diameter of the steel wire is 0.60 mm and the length of the bar AB is 0.20 m. When a mass of 10 kg is suspended from the centre of AB bar remains horizontal. (i) What is the tension in each wire? (ii) Calculate the extension of the steel wire and the energy stored in it. (iii) Calculate the diameter of the brass wire. (iv) If the brass wire were replaced by another brass wire of diameter 1 mm, where should the mass be suspended so that AB would remain horizontal? The Young modulus for steel = 2.0 ×10¹¹ Pa, the Young modulus for brass = 1.0 ×10¹¹ Pa. 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 50 N; extension=1.8×10⁻³ m; energy=0.045 J; brass diameter=8.4×10⁻⁴ m; x=0.12 m. Therefore the correct answer is A.