Question

a wire of length 470 cm and cross section 3.0×10^-9cm^2 stretches by the same amount as a copper wire of length 350 cm and cross section 4.0×10^-9cm^2.find the ratio of youngs modulus of steel to that of a copper.......



pls answer fast its toooo urgent

Answer 1

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?

Answer 2

Answer:

Y₁ : Y₂ = 9 : 5

Explanation:

Given :

For steel wire :

A₁ = 3 × 10⁻⁵ m³  and l₁ = 4.7 m

For copper wire :

A₂ =  4 × 10⁻⁵ m³  and l₂ = 3.5 m

It is said as :

Δl₁ = Δl₂ = Δl  and  F₁ = F₂ = F

We know :

Y₁ =  F₁ l₁ / A₁ Δl₁

= > F /  3 × 10⁻⁵ × 4.7 /Δl

Also Y₂ = F₂ l₂ / A₂ Δl₂

Y₂ = F /  4 × 10⁻⁵ m³ × 3.5 / Δl

We have find ratio of Y₁ / Y₂

Y₁ : Y₂ = ( F /  3 × 10⁻⁵ × 4.7 /Δl ) / ( F /  4 × 10⁻⁵ m³ × 3.5 / Δl )

Y₁ : Y₂ = 4 × 10⁻⁵ × 4.7 / 3 × 10⁻⁵ × 3.5 )

Y₁ : Y₂ = 18.5 / 10.5 ≈ 1.8

Y₁ : Y₂ = 18 / 10 .

Y₁ : Y₂ = 9 : 5

Hence the ratio of the Young's modulus of steel to that of copper 9 : 5