A steel wire of length 4.7 m and cross-sectional area 3.0 × 10-5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10–5 m2 under a given load. What is the ratio of the Young’s modulus of steel to that of copper?

Solution

Length of steel wire, L_s= 4.7m
Length of copper wire, L_c=3.5m
Area of cross-section of steel wire, A_s=3.0 x 10^-5m²Area of copper wire, A_c= 4.0 x 10^-5m²To find = the ratio of Young's modulus of steel to that of copper?

${ΔL}_{s} = {ΔL}_{c} and F_{s} = F_{c} Y o u n g' s m o d u l u s i s g i v e n b y, Y = \frac{F}{A} \frac{L}{ΔL} ∴ \frac{Y_{s}}{Y_{c}} = (\frac{F_{s}}{A_{s}} \frac{L_{s}}{{ΔL}_{s}}) (\frac{A_{c}}{F_{c}} \frac{{ΔL}_{c}}{L_{c}}) = \frac{L_{s}}{L_{c}} \frac{A_{c}}{A_{s}} = \frac{4.7 \times 4.0 \times 10^{- 5}}{3.5 \times 3.0 \times 10^{- 5}} = 1.8$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

A steel wire of length 4.7 m and cross-sectional area 3.0 × 10-5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10–5 m2 under a given load. What is the ratio of the Young’s modulus of steel to that of copper?

Some More Questions From Mechanical Properties of Fluids Chapter

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