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

Answer:

50 cm

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,

$\Delta L = L\times \alpha \times \Delta T$

$0.5\times 10^{-2} = 1\times \alpha \times \Delta T$    .... (1)

Let the expansion in length of rod is ΔL.

So,

$\Delta L = 100\times \alpha \times \Delta T$    .... (2)

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

$\frac{\Delta L}{0.5\times 10^{-2}}=\frac{100}{1}$

ΔL = 0.5 m = 50 cm