Young's modulus experiment is performed on a steel wire of 1 m length and 8 mm diameter. The mass required to be added in the experiment to produce 5 mm elongation of the wire is (Y text steel =2 × 109 Nm -2, g=10 m / s 2)

Question

Young's modulus experiment is performed on a steel wire of 1 m length and 8 mm diameter. The mass required to be added in the experiment to produce 5 mm elongation of the wire is (Y text steel =2 × 109 Nm -2, g=10 m / s 2) (A) 25 kg (B) 50 kg (C) 250 kg (D) 500 kg

Tardigrade Admin · Accepted Answer

Given, L =1 m , r=(a/2)=4 mm =4 × 10-3 m Δ l =5 mm =5 × 10-3 m Y =(m g L/π r2 Δ l) ⇒ m=(Y π r2 Δ l/g L) = (2 × 109 × 3.14 ×(4 × 10-3)2 ×(5 × 10-3)/10 × 1) =(2 × 3.14 × 16 × 5/10) =50.24 kg ≈ 50 kg

Q. Young's modulus experiment is performed on a steel wire of 1m length and 8mm diameter. The mass required to be added in the experiment to produce 5mm elongation of the wire is (Ysteel ​=2×109Nm−2,g=10m/s2)

25 kg

50 kg

250 kg

500 kg

Given, L=1m,r=2a​=4mm=4×10−3m Δl=5mm=5×10−3m Y=πr2ΔlmgL​ ⇒m=gLYπr2Δl​ =10×12×109×3.14×(4×10−3)2×(5×10−3)​ =102×3.14×16×5​ =50.24kg≈50kg

Q. Young's modulus experiment is performed on a steel wire of $1 m$ length and $8 mm$ diameter. The mass required to be added in the experiment to produce $5 mm$ elongation of the wire is $(Y_{steel} = 2 \times 1 0^{9} N m^{- 2}, g = 10 m / s^{2})$