To solve the question regarding the coefficient of cubical expansion, we need to follow these detailed steps:
### Step 1: Understand the Given Data
The problem states that the coefficient of linear expansion of a material is [tex]\(5 \times 10^{-5}\)[/tex] per °F.
### Step 2: Convert the Coefficient of Linear Expansion from °F to °C
The relation between Fahrenheit temperature scale (°F) and Celsius temperature scale (°C) can be given as:
[tex]\[ 1 \, \text{°F} = \frac{5}{9} \, \text{°C} \][/tex]
Therefore, to convert the coefficient of linear expansion (α) from per °F to per °C, we multiply it by [tex]\(\frac{9}{5}\)[/tex].
[tex]\[ \alpha_{C} = \alpha_{F} \times \frac{9}{5} \][/tex]
[tex]\[ \alpha_{C} = 5 \times 10^{-5} \times \frac{9}{5} \][/tex]
[tex]\[ \alpha_{C} = 9 \times 10^{-5} \, \text{per °C} \][/tex]
### Step 3: Calculate the Coefficient of Cubical Expansion
It is known that the coefficient of cubical expansion (β) is approximately three times the coefficient of linear expansion (α).
[tex]\[ \beta_{C} = 3 \times \alpha_{C} \][/tex]
[tex]\[ \beta_{C} = 3 \times 9 \times 10^{-5} \][/tex]
[tex]\[ \beta_{C} = 27 \times 10^{-5} \][/tex]
[tex]\[ \beta_{C} = 0.00027 \, \text{per °C} \][/tex]
### Step 4: Match the Result with the Given Options
From the calculations, we found that the coefficient of cubical expansion per °C is [tex]\(0.00027\)[/tex].
Comparing with the given options:
1) [tex]\(0.000018 \, \text{per °C}\)[/tex]
2) [tex]\(0.00027 \, \text{per °C}\)[/tex]
3) [tex]\(0.00009 \, \text{per °C}\)[/tex]
4) [tex]\(0.000015 \, \text{per °C}\)[/tex]
The correct option is:
[tex]\[ \boxed{0.00027\, \text{per }^\circ \text{C}} \][/tex]
Therefore, the coefficient of cubical expansion of the material expressed per °C is:
[tex]\[ \boxed{0.00027 \, \text{per °C}} \][/tex]
