A steel wire of length 4.7 m and cross-sectional area 3 × 10-5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10-5 m 2 under a given load. The ratio of Young's modulus of steel to that of copper is

Question

A steel wire of length 4.7 m and cross-sectional area 3 × 10-5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10-5 m 2 under a given load. The ratio of Young's modulus of steel to that of copper is (A) 1.2 (B) 1.4 (C) 1.6 (D) 1.8

Tardigrade Admin · Accepted Answer

Y=(F l/A ⋅ Δ l) or Δ l=(F ⋅ l/A ⋅ Y) ⇒ Δ l=(F ⋅ lS/AS ⋅ YS) =(F ⋅ lC/AC ⋅ YC) ⇒ (YS/YC)=(lS ⋅ AC/AS ⋅ lC) =((4.7 m ) ×(4 × 10-5 m 2)/(3 × 10-5 m 2) ×(3.5 m ))=1.8

Q. A steel wire of length 4.7 m and cross-sectional area 3×10−5m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0×10−5m2 under a given load. The ratio of Young's modulus of steel to that of copper is

1.2

1.4

1.6

1.8

Y=A⋅ΔlFl​ or Δl=A⋅YF⋅l​ ⇒Δl=AS​⋅YS​F⋅lS​​ =AC​⋅YC​F⋅lC​​ ⇒YC​YS​​=AS​⋅lC​lS​⋅AC​​ =(3×10−5m2)×(3.5m)(4.7m)×(4×10−5m2)​=1.8

Q. A steel wire of length 4.7 m and cross-sectional area $3 \times 1 0^{- 5} m^{2}$ stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of $4.0 \times 1 0^{- 5} m^{2}$ under a given load. The ratio of Young's modulus of steel to that of copper is