Linear Expansion of Solid Numericals Class 8

The linear expansion of a solid is an increase in the length of a wire or a rod of a solid due to an increase in its temperature. In this post, we will study related formulas and solve a numerical problem based on this the linear expansion of a solid.

Formulas Used

Change in length ΔL= α L₁ ΔT………………. (1)

final length L₂ = L₁ + α L₁ ΔT
=>L₂ = L₁(1 + α ΔT) …………… (2)

α = coefficient of linear expansion of the solid substance
α = (L₂ – L₁) /(L₁ ΔT) …………. (3)

Numericals on Linear Expansion of Solid Class 8

Question: What will be the increase in length of a steel rod of length 0.5 m, when its temperature is increased by 60 ⁰C? The coefficient of linear expansion of steel is 0.000013 (1/⁰C).

Solution:

Given : Initial length of the rod = 0.5 m, change in temperature = 60 ⁰C,
change in length = ΔL = ?

Using formula ΔL= α L₁ ΔT = = 0.000013 x 0.5 x 60 = 0.00039 m

Increase in length = 0.039 cm