# 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 L_{1} ΔT………………. (1)

final length L_{2} = L_{1} + α L_{1} ΔT

=>L_{2} = L_{1}(1 + α ΔT) …………… (2)

α = coefficient of linear expansion of the solid substance

α = (L_{2} – L_{1}) /(L_{1} 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 ^{0}C? The coefficient of linear expansion of steel is 0.000013 (1/^{0}C).**

Solution:

Given : Initial length of the rod = 0.5 m, change in temperature = 60

^{0}C,

change in length = ΔL = ?Using formula ΔL= α L

_{1}ΔT = = 0.000013 x 0.5 x 60 = 0.00039 m

Increase in length = 0.039 cm