Two rods are both precisely 10.000 cm long. Rod "A" is made of aluminum, while Rod "B" is made of steel. The linear expansion coefficient "alpha" is twice as large for aluminum (24 x 10^-6 K^-1) than for steel (12 x 10^-6 K^-1).

If Rod "A" is heated up by 10 degrees C, and Rod "B" is heated up by 20 degrees C, which one will be longer?

A) The aluminum rod ("A")

B) The steel rod ("B")

C) They will expand by the same amount,

C) They will expand by the same amount

Explanation:

Given;

original length of both rods, L₁ = 10 cm

linear expansion coefficient of rod A, α = 24 x 10⁻⁶ K⁻¹

temperature of rod A, θ = 10 °C

linear expansion coefficient of rod B, α = 12 x 10⁻⁶ K⁻¹

temperature of rod B, θ = 20 °C

Increase in length for each rod is calculated as follows:

Rod "A" which is made of aluminum

L₂ = L₁ (1 + αθ)

L₂ = 10 (1 + 24 x 10⁻⁶ x 10)

L₂ = 10 (1 + 24 x 10⁻⁵)

L₂ = 10 (1.00024)

L₂ = 10.0024 cm

Rod "B" which is made of steel

L₂ = L₁ (1 + αθ)

L₂ = 10 (1 + 12 x 10⁻⁶ x 20)

L₂ = 10 (1 + 24 x 10⁻⁵)

L₂ = 10 (1.00024)

L₂ = 10.0024 cm

The two rods expanded by the amount.

Correct option is C; "They will expand by the same amount"