Chapter 2, Problem 2STP

Which value is NOT equivalent to the others?
A. 500 m
C. 5000 cm
B. 0.5 km
D. $5\times {10}^{11}nm$

Interpretation Introduction

Interpretation:

The value which is not equivalent to the others needs to be determined.

Concept introduction:

Ratio of an equivalent values (or standards) having different units is defined as conversion factor, used in dimensional analysis. A systematic method to solve questions that uses conversion factor to convert, or move/change from one particular unit to other different units is described as dimensional analysis.

Answer to Problem 2STP

Correct answer: The correct option is (c).

Explanation of Solution

Reason for correct option: A conversion factor accomplishes following two things:

First one, it must cancel one unit. Second one, introduce a new one.

Put the given value, $5000\text{cm}$, into base SI unit, meter

To convert cm into m, formula $\text{m = }\frac{\text{cm}}{\text{100}\text{.00}}$ is used. Apply the formula, $\text{m = }\frac{\text{cm}}{\text{100}\text{.00}}=\frac{5000}{100.00}=50$

After putting the given values into base SI unit, meters, the correct option is (c).

Conclusion

Reasons for incorrect options: To check the correct answer put the given values into base SI unit, kilometers.

Option (a):The given value is $\text{500}\text{m}$. This value is equals to $\text{500}\text{m}$. Hence, this is an incorrect option.

Option (b):The given value is $\text{0}\text{.5}\text{km}$.

To convert km into m, formula $\text{m = }\frac{\text{km}}{\text{0}\text{.0010000}}$ is used. Apply the formula, $\text{m = }\frac{\text{0}\text{.5}}{\text{0}\text{.0010000}}=500$. This value is equals to $\text{500}\text{m}$. Hence, this is an incorrect option.

Option (d):The given value is $\text{5}\times {\text{10}}^{11}\text{nm}$. Since, $\text{1 m = 1000000000 nm}$. This value is equals to $\text{500}\text{m}$. Hence, this is an incorrect option.