Two solid rods have the same length and are made of the same material with circular cross sections. Rod 1 has a radius 1 and Rod 2 has a radius 2=1/2 . If a compressive force is applied to both rods, their lengths are reduced by Δ1 and Δ2 , respectively.

Complete Question:

Two solid rods have the same length and are made of the same material with circular cross sections. Rod 1 has a radius r, and rod 2 has a radius r / 2. If a compressive force F is applied to both rods, their lengths are reduced by ΔL1 and ΔL2, respectively. The ratio ΔL1 / ΔL2 is equal to.

Explanation:

Since the two rods have the same length, L₁ = L₂ = L

Radius of rod 1, r₁ = r

Radius of rod 2, r₂ = r/2

Cross sectional area of rod 1,

Cross sectional area of rod 2,

The same compressive force is applied to the two rods, F₁ = F₂ = F

The rods are said to be made of the same material, this means that they have the same young's modulus.

Young's modulus of rod 1,

Young's modulus of rod 2,

Since Y₁ = Y₂

..............(*)

Put A₁ and A₂ into (*)

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