Can anybody plz solve the Q in the given attachment asap.. plz
Ans is opn b)
Adeel , 7 Years ago
Grade 12th pass
1 Answers
Arun
Last Activity: 7 Years ago
Initial temperature, T1 = 27°C Length of the brass wire at T1, l = 1.8 m Final temperature, T2 = –39°C Diameter of the wire, d = 2.0 mm = 2 × 10–3 m Tension developed in the wire = F Coefficient of linear expansion of brass, α = 2.0 × 10–5 K–1 Young’s modulus of brass, Y = 0.91 × 1011 Pa Young’s modulus is given by the relation: γ = Stress / Strain = (F/A) / (∆L/L) ∆L = F X L / (A X Y) ……(i)
Where, F = Tension developed in the wire A = Area of cross-section of the wire. ΔL = Change in the length, given by the relation: ΔL = αL(T2 – T1) … (ii) Equating equations (i) and (ii), we get: αL(T2 – T1) = FL / [ π(d/2)2X Y ] F = α(T2 – T1)πY(d/2)2 F = 2 × 10-5 × (-39-27) × 3.14 × 0.91 × 1011 × (2 × 10-3 / 2 )2 = -3.8 × 102 N (The negative sign indicates that the tension is directed inward.) Hence, the tension developed in the wire is 3.8 ×102 N.
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