Question

Suppose a 1 meter long bar expands 0.5 centimeters when heated. By how much will a 100 meter long bar of the same material expand when similarly heated?

Answer 1

50 cm

Step-by-step explanation:

Let the increase i temperature of the metal rod is ΔT and the coefficient of linear expansion of the material of metal rod be ∝.

By use of the formula of linear expansion,

`\Delta L = L* \alpha * \Delta T`

`0.5* 10^(-2) = 1* \alpha * \Delta T` .... (1)

Let the expansion in length of rod is ΔL.

So,

`\Delta L = 100* \alpha * \Delta T` .... (2)

Dividing equation (2) by equation (1), we get

`(\Delta L)/(0.5* 10^(-2))=(100)/(1)`

ΔL = 0.5 m = 50 cm