Deck 1: Systems of Measurement

Question 1

The prefix "giga" means

A) 10¹²
B) 10⁶
C) 10³
D) 10⁹
E) 10¹⁵

Answer 1

10⁹

Question 2

To convert a quantity from m/s to km/h, you must

A) multiply by 1000 and divide by 60.
B) multiply by 1000 and divide by 3600.
C) multiply by 60 and divide by 1000.
D) multiply by 3600 and divide by 1000.
E) None of these is correct.

Answer 2

multiply by 3600 and divide by 1000.

Question 3

To convert a quantity from km/h to m/s, you must

A) multiply by 1000 and divide by 60.
B) multiply by 1000 and divide by 3600.
C) multiply by 60 and divide by 1000.
D) multiply by 3600 and divide by 1000.
E) None of these is correct.

Answer 3

multiply by 1000 and divide by 3600.

Question 4

The prefix "mega" means

A) 10²
B) 10⁹
C) 10^-3
D) 10⁶
E) 10^-6

Question 5

The density of seawater was measured to be 1.07 g/cm³. This density in SI
Units is

A) l.07 $\times$ 10^-3 kg/m³
B) (1/1.07) $\times$ 10³ kg/m³
C) 1.07 $\times$ 10³ kg
D) 1.07 $\times$ 10^-3 kg
E) 1.07 $\times$ 10³ kg/m³

Question 6

The prefix "kilo" means

A) 10¹²
B) 10⁸
C) 10⁶
D) 10³
E) 10¹

Question 7

The fundamental physical quantities are

A) mass, length, time, temperature, amount of a substance, current, and luminous intensity.
B) weight, length, time, temperature, amount of a substance, current, and luminous intensity.
C) mass, length, time, temperature, force, current, and luminous intensity.
D) mass, length, time, force, momentum, amount of a substance, and current.
E) weight, length, time, temperature, amount of a substance, potential energy, and luminous intensity.

Question 8

To convert a quantity from g/cm³ to kg/m³, you must

A) multiply by 0.01.
B) multiply by 100.
C) multiply by 1000.
D) multiply by 0.001.
E) multiply by 1,000,000.

Question 9

Which of the following is NOT one of the fundamental units in the SI system?

A) Newton
B) meter
C) kilogram
D) second
E) All of the above are fundamental units in the SI system.

Question 10

Which of the following is NOT one of the fundamental physical quantities in the SI system?

A) mass
B) length
C) force
D) time
E) All of these are fundamental physical quantities in the SI system.

Question 11

The prefix "micro" means

A) 10^-12
B) 10^-6
C) 10^-3
D) 10^-2
E) 10^-1

Question 12

Which of the following prefixes does NOT represent a fractional part of a whole unit?

A) nano
B) micro
C) kilo
D) milli
E) deci

Question 13

The SI unit for mass is

A) $\mu$ g
B) mg
C) g
D) kg
E) lb

Question 14

Which of the following prefixes does NOT represent a quantity larger than a single unit?

A) kilo
B) mega
C) giga
D) tera
E) femto

Question 15

The prefix "nano" means

A) 10^-12
B) 10^-6
C) 10^-3
D) 10^-2
E) None of these is correct.

Question 16

The prefix "milli" means

A) 10^-12
B) 10^-6
C) 10^-3
D) 10^-2
E) 10^-1

Question 17

The prefix "centi" means

A) 10^-12
B) 10^-6
C) 10^-3
D) 10^-2
E) 10^-1

Question 18

To convert a quantity from km/(hr · s) to m/s², you must

A) multiply by 1000 and divide by 60.
B) multiply by 60 and divide by 3600.
C) multiply by 60 and divide by 1000.
D) multiply by 3600 and divide by 1000.
E) None of these is correct.

Question 19

Which of the following is a fundamental unit of the SI system of units?

A) kilometer
B) joule
C) kilogram
D) gram
E) newton

Question 20

The prefix "pico" means

A) 10^-12
B) 10^-6
C) 10^-3
D) 10⁶
E) 10⁹

Question 21

In doing a calculation, you end up with a fraction having m/s in the numerator and m/s² in the denominator. The result will have units of

A) m²/s³
B) s^-1
C) s³/m²
D) s
E) m/s

Question 22

Compute:

A) 3.3 $\times$ 10^-6
B) 5.1 $\times$ 10⁶
C) 5.1 $\times$ 10^-12
D) 3.3 $\times$ 10^-1
E) None of these is correct.

Question 23

When we look up in the sky the Sun appears about as big as the moon; however, we know that the Sun is much further away. Given that the radius of the Sun is about 7 $\times$ 10⁸ m and that the radius of the moon is about 2 $\times$ 10⁶ m, calculate approximately the number of times the moon could fit inside the Sun.

A) 4 $\times$ 10²
B) 4 $\times$ 10⁶
C) 4 $\times$ 10⁷
D) 1 $\times$ 10⁵
E) 2 $\times$ 10⁵

Question 24

In doing a calculation, you arrive at an expression in which the numerator is in kilometers and the denominator is in meters per second. When the calculation is completed, the result will be in units of

A) meters, if you divide by 1000.
B) meters, if you multiply by 1000.
C) seconds, if you divide by 1000.
D) seconds, if you multiply by 1000.
E) meters squared per second, if you multiply by 1000.

Question 25

If v and t represent velocity and time, respectively, C₂ in v = C₁e^-C2^t must

A) have the dimensions L/T.
B) have the dimensions 1/T.
C) have the dimensions L/T ².
D) have the dimensions L²/T ².
E) be dimensionless.

Question 26

If x and t represent position and time, respectively, the B in x = A cos Bt must

A) have the dimensions L/T.
B) have the dimensions 1/T.
C) have the dimensions L.
D) have the dimensions L²/T ².
E) be dimensionless.

Question 27

Evaluate:

A) 1.1 $\times$ 10⁵
B) 1.7 $\times$ 10^-4
C) 3.6 $\times$ 10^-8
D) 4.5 $\times$ 10⁵
E) 1.1

Question 28

If x and t represent position and time, respectively, the A in x = A cos Bt must

A) have the dimensions L/T.
B) have the dimensions 1/T.
C) have the dimensions L.
D) have the dimensions L²/T ².
E) be dimensionless.

Question 29

In Newton's Law of Gravity the universal gravitational constant G = Fr²/m₁m₂, where F is the gravitational force between the two masses, m₁ and m₂, and r is the distance between them. What are the dimensions of G?

A) L²M^-1T ²
B) L³M^-1T ^-2
C) L²M^-2T ^-2
D) L³M^-1T ²
E) L^-3M¹T ³

Question 30

The density of an object equals its mass divided by its volume. The mass of Earth is 6 $\times$ 10²⁴ kg and its radius is 4 $\times$ 10³ miles. The mass of the Sun is 2 $\times$ 0 10³³ g and its radius is 7 $\times$ 10⁵ km. Calculate the Earth's density divided by that of the Sun.

A) 4 $\times$ 10^-1
B) 4 $\times$ 10^-2
C) 4 $\times$ 10⁰
D) 4 $\times$ 10¹
E) none of the above

Question 31

If v and t represent velocity and time, respectively, C₁ in v = C₁e^-C2^t must

A) have the dimensions L/T.
B) have the dimensions L²/T.
C) have the dimensions L/T ².
D) have the dimensions L²/T ².
E) be dimensionless.

Question 32

If K has dimensions ML²/T ², the k in K = kmv ² must

A) have the dimensions ML/T ².
B) have the dimensions M.
C) have the dimensions L/T ².
D) have the dimensions L²/T ².
E) be dimensionless.

Question 33

The dimensions of two quantities MUST be identical if you are either __________ or __________ the quantities.

A) adding; multiplying
B) subtracting; dividing
C) multiplying; dividing
D) adding; subtracting
E) All of these are correct.

Question 34

If x and t represent distance and time, respectively, the C in x = ¹/2Ct ² must

A) have the dimensions ML/T ².
B) have the dimensions M.
C) have the dimensions L/T ².
D) have the dimensions L²/T ².
E) be dimensionless.

Question 35

The dimensions of mass density are

A) MLT ^-1
B) ML³
C) ML²
D) ML^-1
E) None of these is correct.

Question 36

Compute:

A) 1 $\times$ 10¹⁷
B) 6 $\times$ 10⁷
C) 8 $\times$ 10¹⁷
D) 4 $\times$ 10⁷
E) None of these is correct.

Question 37

The dimensions of energy, E, are ML²/T ². Using dimensional analyzes, E is the product of which two quantities?

A) Mass divided by time squared
B) Force times acceleration
C) Mass times acceleration
D) force times distance
E) force divided by time squared

Question 38

You are traveling at a speed of 80 km/hr. Your speed in mph is approximately

A) 30
B) 40
C) 50
D) 60
E) 70

Question 39

In the expression F_net = ma, m must have the dimensions

A) ML/T ²
B) M
C) L/T ²
D) L/T
E) ML²/T ²

Question 40

Evaluate:
(4)0 $\times$ 10^-6)(3.0 $\times$ 10⁴)

A) 12 $\times$ 10¹⁰
B) 1.2 $\times$ 10^-10
C) 12 $\times$ 10^-5
D) 1.2 $\times$ 10^-1
E) 12 $\times$ 10^-10

Question 41

Light travels at 3 $\times$ 10⁸ m/s, and the size of a proton is about 1 fm. Calculate the order of magnitude for the time taken for light to pass across a proton.

A) 10^-7 s
B) 10^-8 s
C) 10^-22 s
D) 10^-23 s
E) 10²³ s

Question 42

The mass of an electron is of the order of 10^-30 kg and the mass of the universe is believed to be of the order of 10⁵² kg. From this information you can conclude that

A) the mass of Earth is 52 orders of magnitude greater than that of the electron.
B) the mass of Earth is 30 orders of magnitude greater than that of the electron.
C) the mass of the electron is 82 orders of magnitude greater than that of Earth.
D) the mass of Earth is 82 orders of magnitude greater than that of the electron.
E) the mass of the electron is 30 orders of magnitude greater than that of Earth.

Question 43

The momentum of a body is defined to be the product of its mass and its velocity. If the mass of an air-track glider is known to be 225 g and its velocity is measured to be 3.1 cm/s, its momentum should be reported as

A) 697.5 g · cm/s
B) 698 g · cm/s
C) 7.0 $\times$ 10² g · cm/s
D) 6.98 $\times$ 10² g · cm/s
E) 6.975 $\times$ 10² g · cm/s

Question 44

What is the order of magnitude of Earth's tallest mountain heights?

A) 10⁸ m
B) 10⁴ m
C) 10⁶ m
D) 10³ m
E) 10⁵ m

Question 45

Estimate the number of raindrops needed to fill a volume of 1m $\times$ 1m $\times$ 1cm.

A) 10³
B) 10⁵
C) 10⁷
D) 10⁹
E) 10¹¹

Question 46

The chemical agent dioxin can be toxic or hazardous to humans in concentrations as small as one part per billion. If I am testing a soil sample that has a mass of 1.0 kg, how much dioxin would have to be present for me to label it toxic or hazardous?

A) a picogram
B) a kilogram
C) a microgram
D) a milligram
E) a nanogram

Question 47

If Earth is approximately 4.5 billion years old, estimate the order of magnitude for the number of times it has rotated about its own axis. (Assume a constant rate of rotation.)

A) 10⁹
B) 10¹⁰
C) 10¹¹
D) 10¹²
E) 10¹⁴

Question 48

An impurity in a manufacturing process will cause a batch to be rejected if the impurity exceeds one part per million. What is the maximum amount of impurity that could be present if the batch contains 100 kg of the product?

A) 100 micrograms
B) 100 nanograms
C) 100 grams
D) 100 megagrams
E) 100 milligrams

Question 49

The size of a proton is of the order of 10^-15 m and the size of the visible universe is of the order of 10²⁶ m. From this information you can conclude that

A) the size of the universe is 26 orders of magnitude greater than that of the proton.
B) the size of the universe is 41 orders of magnitude greater than that of the proton.
C) the size of the proton is 11 orders of magnitude greater than that of the universe.
D) the size of the universe is 15 orders of magnitude greater than that of the proton.
E) the size of the proton is 15 orders of magnitude greater than that of the universe.

Question 50

The net force acting on a body is defined to be the product of the mass of the body and its resultant acceleration. If the mass of a body is known to be 184 kg and its acceleration is measured to be 2.4 m/s², the resultant force should be reported as

A) 4.4 $\times$ 10² kg · m/s²
B) 441.6 kg · m/s²
C) 442 kg · m/s²
D) 4.416 kg · m/s²
E) 4.42 $\times$ 10² kg · m/s²

Question 51

Earth's population, expressed as an order of magnitude, is closest to

A) 10⁶
B) 10¹⁰
C) 10⁵
D) 10⁸
E) 10⁷

Question 52

Light travels at 3 $\times$ 10⁸ m/s, and it takes about 8 min for light from the sun to travel to Earth. Based on this, the order of magnitude of the distance from the sun to Earth is

A) 10¹⁰ m
B) 10⁸ m
C) 10⁹ m
D) 10⁶ m
E) 10¹¹ m

Question 53

Compute:
(12 $\times$ 10⁶ - 2 $\times$ 10⁷) / (-12 $\times$ 10⁷ + 7 $\times$ 10⁶)

A) 7.1 $\times$ 10^-2
B) 7.0 $\times$ 10⁶
C) 2.0 $\times$ 10^-8
D) -7.1 $\times$ 10^-2
E) 2 $\times$ 10⁵

Question 54

The measurement 5.130 $\times$ 10^-4 has _____ significant figures.

A) two
B) three
C) one
D) seven
E) four

Question 55

Which of the following represents a value of current measured to at least five significant figures?

A) 2.375 $\times$ 10⁴ A
B) 0.00347 A
C) 3.0 $\times$ 10⁵ A
D) 23.75 $\times$ 10¹ A
E) 50.300 A

Question 56

The measurement 23.0040 has _____ significant figures.

A) six
B) three
C) five
D) four
E) two

Question 57

A person inhales about 1 L of air per breathe. Estimate the number of air molecules inhaled.

A) 10¹⁰
B) 10¹⁴
C) 10¹⁸
D) 10²²
E) 10²⁶

Question 58

The longest bridge on Earth is of the order of

A) 10³ m
B) 10⁴ m
C) 10⁵ m
D) 10⁶ m
E) 10⁷ m

Question 59

If you have a music CD collection of about 150 discs, estimate the order of magnitude of the number of heartbeats you would have if you listened all the way through your collection.

A) 10⁶
B) 10⁸
C) 10¹⁰
D) 10⁴
E) 10³

Question 60

The number of seconds in a month is of the order of

A) 10³
B) 10⁸
C) 10⁵
D) 10¹⁰
E) 10⁶

Question 61

What angle does the vector 1 make with the positive z axis?

A) 55.5º
B) 45.0º
C) 64.9º
D) 34.5º
E) 25.1º

Question 62

Given vector $$\vec{A} \quad \text{ }$$ , the vector 3 $$\vec{A} \quad \text{ }$$

A) has a magnitude 3 times that of $$\vec{A} \quad \text{ }$$ .
B) points in the same direction as $$\vec{A} \quad \text{ }$$ .
C) has components each of which is 3 times those of $$\vec{A} \quad \text{ }$$ .
D) makes the same angle with a given axis as does $$\vec{A} \quad \text{ }$$ .
E) is described by all of these.

Question 63

The vector in the figure that could represent the vector - is

A)
B)
C)
D)
E)

Question 64

What is the least number of non-zero vectors that can be added to give a resultant equal to zero?

A) 2
B) 3
C) 4
D) 5
E) It cannot be done.

Question 65

The vector equation that describes the relationship among vectors , , and is

A) = +
B)
C) = -
D) = -
E) = +

Question 66

A diehard music lover still prefers to listen to his vinyl records, which rotate at 33 revolutions per minute. If he listens for an average of three hours per day, estimate the order of magnitude for the number of revolutions his turntable makes in a year.

A) 10⁷
B) 10²
C) 10⁶
D) 10⁵
E) 10⁴

Question 67

The angle between vectors $$\vec{A} \quad$$ and $$\vec{B} \quad$$ is 30º, and their sum is $$\vec{C} \quad$$ . Which vector diagram correctly describes the vectors $$\vec{A} \quad$$ , $$\vec{B} \quad$$ , and $$\vec{C} \quad$$ ?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 68

Two vector quantities, whose directions can be altered at will, can have a resultant of any magnitude between the limits 0 and 200. The magnitude of each vector quantity must therefore be

A) between 0 and 80.
B) between 120 and 200.
C) less than 100.
D) exactly 100.
E) more than 100.

Question 69

The components of a vector are A_x = -10 units and A_y = 6 units. What angle does this vector make with the positive x axis?

A) 31º
B) -31º
C) 180º - 31º
D) 180º + 31º
E) 90º - 31º

Question 70

A car proceeding due south at 60 km/h ( ₁) makes a right turn, after which it is traveling due west at 80 km/h ( ₂). What is its change in velocity ( ₂ - ₁)?

A) 100 km/h 37º north of west
B) 100 km/h 37º south of west
C) 20 km/h west
D) 20 km/h 37º north of west
E) 20 km/h 37º south of west

Question 71

Three vectors have the following x and y components:
The angle that the resultant makes with the positive direction of the x axis is

A) 1.2º
B) 36º
C) 50º
D) 40º
E) 70º

Question 72

Vectors and have the following components:

The angle between the positive x axis and the vector - is

A) -45º
B) 194º
C) 37º
D) -54º
E) 86º

Question 73

Two vectors and are added to give a resultant . The components of are A_x = -8.0 units and A_y = 6.0 units and the components of are B_x = 1.0 units and B_y = -1.0 units. The magnitude of vector is

A) -1.0 units
B) +8.6 units
C) +19 units
D) +2.0 units
E) -3.2 units

Question 74

A vector of magnitude 5 points in the +y direction. Another vector of magnitude 4 is added to the first vector. The largest possible magnitude of the sum is

A) 1
B) 4
C) 5
D) 9
E) 10

Question 75

What angle does the vector make with the positive x axis?

A) 67.4º
B) 22.6º
C) 36.9º
D) 53.1º
E) 24.6º

Question 76

Which of the following vector equations correctly describes the relationship among the vectors shown in the figure?

A)
B) - + = 0
C) - - = 0
D) + + = 0
E) None of these equations is correct.

Question 77

Vector has components A_x = +4.0 units and A_y = +3.2 units, whereas vector has components B_x = +2.5 units and B_y = +5.5 units. The angle between the two vectors is

A) 24º
B) 65º
C) 27º
D) 39º
E) 14º

Question 78

The length of the vector is

A) 169 units
B) 144 units
C) 25 units
D) 17 units
E) None of these is correct.

Question 79

Two vector quantities, whose directions can be altered at will, can have a resultant between the limits 5 and 15. The magnitudes of these two vector quantities could be

A) 2 and 2
B) 5 and 10
C) 20 and 40
D) 20 and 50
E) 59 and 97

Question 80

A velocity vector has an x component of +5.5 m/s and a y component of -3.5 m/s. The diagram that gives the direction of the vector is

A) 1
B) 2
C) 3
D) 4
E) None of these is correct.