Question

question 08: which expression shows the correct cancellation of units in dimensional analysis? a. (10 m)(100 cm/m) = 1000 cm b. (10 m)(100 cm) = 1000 m c. (10 m)/(100 cm) = 0.1 m d. (10 m)/(100 cm/m) = 0.1 m question 09: what does the term dimensional homogeneity mean? a. all terms in an equation have the same dimensions b. an equation has different units on each side

Explanation:

Step1: Recall unit - conversion factor

We know that 1 m = 100 cm, or the conversion factor is $\frac{100\ cm}{1\ m}$.

Step2: Analyze option a

When we multiply (10 m) by $\frac{100\ cm}{1\ m}$, the'm' units cancel out: $(10\ m)\times\frac{100\ cm}{1\ m}=10\times100\ cm = 1000\ cm$. This is the correct way of using dimensional - analysis for unit conversion.

Step3: Analyze option b

$(10\ m)(100\ cm)$ is incorrect because we are not using a proper conversion factor. The units do not cancel out correctly, and the result $1000\ m$ is wrong.

Step4: Analyze option c

$(10\ m)/(100\ cm)$ is incorrect. Since 100 cm = 1 m, $(10\ m)/(1\ m)=10$, not $0.1\ m$.

Step5: Analyze option d

$(10\ m)/(100\ cm/m)$ is incorrect. The units do not cancel out in a meaningful way to get $0.1\ m$.

For question 09:
The concept of dimensional homogeneity means that all terms in an equation have the same dimensions. This is a fundamental principle in dimensional analysis. If the dimensions of the terms in an equation are not the same, the equation is not physically valid.

Answer:

Question 08: A. (10 m)(100 cm/m) = 1000 cm
Question 09: A. All terms in an equation have the same dimensions