Q56P - Fundamentals Of Physics

Question

The corn–hog ratio is a financial term used in the pig market and presumably is related to the cost of feeding a pig until it is large enough for market. It is defined as the ratio of the market price of a pig with a mass of 3.108 slugs to the market price of a U.S. bushel of corn. (The word “slug” is derived from an old German word that means “to hit”; we have the same meaning for “slug” as a verb in modern English.) A U.S. bushel is equal to 35.238 L. If the corn–hog ratio is listed as 5.7 on the market exchange, what is it in the metric units of,

                                               $\frac{\mathrm{price} \mathrm{of} 1 \mathrm{kilogram} \mathrm{of} \mathrm{pig}}{\mathrm{price} \mathrm{of} 1 \mathrm{liter} \mathrm{of} \mathrm{corn}}?$

(Hint: See the Mass table in Appendix D.)

Step-by-Step Solution

Answer

The Corn-hog ratio in the metric units is $4.4.$

Step 1: Given data

The corn–hog ratio is the ratio of the market price of a pig with a mass of 3.108 slugs to the market price of a U.S. bushel of corn.

The listed corn-hog ratio is 5.7.

Step 2: Understanding the unit conversion

Chain-link conversions are used for unit conversion in which given values are multiplied successively by conversion factors.

Step 3: Converting the given quantities into the required units

Use the conversion factor to convert the quantity in the required unit and find the ratio.

 

Conversion factor is $1 sIug=14.59 kg$

 

Therefore, the mass of the pig is,

$$\begin{gathered} 3.108slugs=\left(3.108\right)\left(14.59\right) \\ =45.346kg \end{gathered}$$

The conversion factor is $1 Bushel=35.238.$

Step 4: Determination of the Corn-hog ratio

The Corn hog ratio is given as,$=\frac{\left(price of 3.108slugs of pig\right)}{\left(price of 1 Bushel of corn\right)}$

Substitute the values to calculate the ratio.

$$\begin{gathered} The Corn hog ration=\frac{\left(45.346kg\right)}{\left(35.238kg\right)} \\ =5.7 \end{gathered}$$

Multiply the equation by the ratio price of 1 kg of pig and price of 1 liter of corn.

$$\begin{gathered} \frac{\left(45.346\times price of 1 kg of pig\right)}{\left(35.238\times price of 1 liter of corn\right)}=5.7 \\ 1.287\times \frac{\left(price of 1 kg of pig\right)}{\left(price of 1 liter of corn\right)}=5.7 \\ \left(\frac{price of 1 kg of pig}{price of 1 liter of corn} \right)=\frac{5.7}{1.287} \\ =4.4 \end{gathered}$$

Thus, the Corn-hog ratio is 4.4