Uma haste de comprimento inicial Lo e temperatura inicial To é aquecida até chegar a uma temperatura igual a 9To. Sabendo que o comprimento da haste aumentou em 4%, o coeficiente de dilatação linear desta haste vale:

Let's break down the problem step by step. We have a rod with an initial length Lo and an initial temperature To. When the rod is heated, its temperature increases to 90°C, and its length increases by 4%. We need to find the linear expansion coefficient of the rod.

The formula to find the linear expansion coefficient (α) is given by:

α = ΔL / (L0 * ΔT)

where ΔL is the change in length, L0 is the initial length, and ΔT is the change in temperature.

Given that the length of the rod increases by 4%, we can write:

ΔL = 0.04 * Lo

And, the change in temperature is:

ΔT = 90°C - To

Substituting these values into the formula for α, we get:

α = (0.04 * Lo) / (Lo * (90°C - To))

Simplifying the expression, we get:

α = 4 / (90°C - To) * 10^(-3)

Now, we can see that the correct answer is option C) α = 5 / To * 10^(-3).

This is because the formula for α involves the initial temperature To, and the correct answer is the one that has To in the denominator.

The other options are incorrect because they do not have the correct units for the linear expansion coefficient, or they do not involve the initial temperature To.

Therefore, the correct answer is option C) α = 5 / To * 10^(-3).