Question 1

John and Linda are arguing about the definition of density. John says the density of an object is proportional to its mass. Linda says the object's mass is proportional to its density and to its volume. Which one, if either, is correct?
A)They are both wrong.
B)John is correct, but Linda is wrong.
C)John is wrong, but Linda is correct.
D)They are both correct.
E)They are free to redefine density as they wish.

Accepted Answer

Density is defined as mass per unit volume, which means it is proportional to mass (as John says) and also that mass is proportional to density and volume (as Linda says), making both of their statements correct.

Question 2

Which one of the quantities below has dimensions equal to  ?
A)mv
B)mv2
C) 
D)mrv
E)

Accepted Answer

C

Question 3

The quantity with the same units as force times time, Ft, with dimensions MLT−1 is
A)mv
B)mvr
C)mv2r
D)ma
E)

Accepted Answer

A

Question 4

Which quantity can be converted from the English system to the metric system by the conversion factor  ?
A)feet per second
B)feet per hour
C)miles per second
D)miles per hour
E)miles per minute

Accepted Answer

The given conversion factor corresponds to converting miles per hour to kilometers per hour in the metric system.

Question 5

The equation for the change of position of a train starting at x = 0 m is given by  . The dimensions of b are
A)T−3
B)LT−3
C)LT−2
D)LT−1
E)L−1T−1

Accepted Answer

The answer of The equation for the change of position...

Question 6

A standard exam page is 8.5 inches by 11 inches. An exam that is 2.0 mm thick has a volume of A)1.9 × 10⁴ mm³. B)4.7 × 10⁴ mm³. C)1.2 × 10⁵ mm³. D)3.1 × 10⁵ mm³. E)3.1 × 10³ mm³.

Accepted Answer

To find the volume, convert the dimensions to millimeters: 8.5 inches = 215.9 mm, 11 inches = 279.4 mm. Volume = 215.9 mm * 279.4 mm * 2.0 mm = 1.2 × 10^5 mm^3.

Question 7

The term  occurs in Bernoulli's equation in Chapter 15, with ρ being the density of a fluid and v its speed. The dimensions of this term are
A)M−1L5T2.
B)MLT2.
C)ML−1T−2.
D)M−1L9T−2.
E)M−1L3T−2.

Accepted Answer

From Bernoulli's equation, 
11eb8c7e_f59f_f20f_8371_bba9512dcd95_TB8847_11 = ρv^2/2
where ρ has dimensions of mass per unit volume (M/L^3) and v has dimensions of velocity (L/T). 
Thus, the dimensions of 11eb8c7e_f59f_f20f_8371_bba9512dcd95_TB8847_11 can be found by substituting the dimensions of ρ and v: 
[M/L^3] * [(L/T)^2]/2 = [M/LT^2] 
Therefore, the answer is C: ML^(-1)T^(-2).

Question 8

Spike claims that dimensional analysis shows that the correct expression for change in velocity,  , is  , where m is mass, t is time, and F is the magnitude of force. Carla says that can't be true because the dimensions of force are  . Which one, if either, is correct?
A)Spike, because  .
B)Spike, because  .
C)Carla, because  .
D)Carla, because  .
E)Spike, because the dimensions of force are  .

Accepted Answer

The correct expression for change in velocity must be dimensionally consistent, meaning that the dimensions of the left side must be equal to those of the right side. From the given expressions, we have:

dimension of Δv = [L]/[T]
dimension of m = [M]
dimension of t = [T]
dimension of F = [M][L]/[T]^2

Applying dimensional analysis to the proposed expression:

Δv = F/m * t

dimension of F/m = [M][L]/[T]^2 /[M] = [L]/[T]^2

dimension of t = [T]

dimension of Δv = [L]/[T]

Therefore, the dimensions of the right side are [L]/[T] * [T] = [L], which do not match the required dimensions of Δv. Carla is correct that the expression proposed by Spike cannot be true because the dimensions of force are not consistent with the dimensions of Δv.

Question 9

The answer to a question is [[MLT−1]]. The question is "What are the dimensions of
A)mr?"
B)mvr?"
C)ma?"
D)mat?"
E)  ?"

Accepted Answer

The answer of The answer to a question is [[MLT−1]]....

Question 10

A rectangle has a length of 1.323 m and a width of 4.16 m. Using significant figure rules, what is the area of this rectangle? A)5.50368 m² B)5.5037 m² C)5.504 m² D)5.50 m² E)5.5 m²

Accepted Answer

The answer of A rectangle has a length of 1.323...

Question 11

The density of an object is defined as
A)the volume occupied by each unit of mass.
B)the amount of mass for each unit of volume.
C)the weight of each unit of volume.
D)the amount of the substance that has unit volume and unit mass.
E)the amount of the substance that contains as many particles as 12 grams of the carbon-12 isotope.

Accepted Answer

The density of an object is the amount of mass for each unit of volume, which is represented by the formula density = mass/volume. Choice A is not correct because it describes the reciprocal of density, which is specific volume. Choice C is incorrect because weight is not the same as mass, and density is defined in terms of mass. Choice D is not a correct definition of density. Choice E describes the concept of Avogadro's number and molar mass, which are not directly related to the definition of density.

Question 12

Which of the following quantities has the same dimensions as kinetic energy,  ? Note: [[a]] = [[g]] = LT−2; [[h]] = L and [[v]] = LT−1.
A)ma
B)mvx
C)mvt
D)mgh
E)mgt

Accepted Answer

The answer of Which of the following quantities has the...

Question 13

Which of the following products of ratios gives the conversion factor to convert miles per hour  to meters per second  ?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which of the following products of ratios...

Question 14

The standard exam page is 8.50 inches by 11.0 inches. Its area in cm² is A)19.5. B)36.8. C)93.5. D)237. E)603.

Accepted Answer

To convert the area from square inches to square centimeters, first convert the dimensions of the page from inches to centimeters (1 inch = 2.54 cm). The dimensions in centimeters are 8.50 inches * 2.54 cm/inch = 21.59 cm by 11.0 inches * 2.54 cm/inch = 27.94 cm. The area in square centimeters is 21.59 cm * 27.94 cm = 603.46 cm^2, which rounds to 603.

Question 15

One U.S. fluid gallon contains a volume of 231 cubic inches. How many liters of gasoline would you have to buy in Canada to fill a 14-gallon tank? (Note: 1 L = 103 cm³.) A)53 B)21 C)14 D)8.0 E)4.0

Accepted Answer

To convert gallons to liters, use the conversion factor: 1 gallon = 3.78541 liters. Therefore, 14 gallons is 14 * 3.78541 = 52.99574 liters, which rounds to 53 liters.

Question 16

If each frame of a motion picture film is 35 cm high, and 24 frames go by in a second, estimate how many frames are needed to show a two-hour-long movie.
A)1400
B)25,000
C)50,000
D)170,000
E)This cannot be determined without knowing how many reels were used.

Accepted Answer

There are 60 minutes in an hour, so a two-hour-long movie is 120 minutes long. To find the number of frames needed, we first need to find the number of seconds in 120 minutes: 120 minutes x 60 seconds per minute = 7200 seconds. Then, we can multiply the number of frames that go by in one second by the number of seconds in the movie: 24 frames per second x 7200 seconds = 172,800 frames. However, this calculation assumes that the movie is shown at a standard frame rate of 24 frames per second. It's possible that a different frame rate was used, which would affect the total number of frames needed. Nonetheless, of the given choices, D is the closest estimate.

Question 17

One number has three significant figures and another number has four significant figures. If these numbers are added, subtracted, multiplied, or divided, which operation can produce the greatest number of significant figures?
A)the addition
B)the subtraction
C)the multiplication
D)the division
E)All the operations result in the same number of significant figures.

Accepted Answer

The answer of One number has three significant figures and...

Question 18

If you drove day and night without stopping for one year without exceeding the legal highway speed limit in the United States, the maximum number of miles you could drive would be closest to
A)8700.
B)300,000.
C)500,000.
D)1,000,000.
E)32,000,000.

Accepted Answer

The legal highway speed limit in the United States varies by state, but the maximum limit is typically around 70-80 miles per hour. Assuming an average speed limit of 75 miles per hour, driving day and night for one year (365 days) would result in a maximum distance of:

75 miles per hour x 24 hours per day x 365 days = 657,000 miles

However, this assumes that there are no stops for fuel, food, or rest, and that there are no delays or detours due to traffic, construction, or other factors. Therefore, the actual distance driven would likely be less than the calculated maximum. A more realistic estimate might be around 500,000 miles.

Question 19

Which of the following products of ratios gives the conversion factors to convert meters per second  to miles per hour  ?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which of the following products of ratios...

Question 20

One mole of the carbon-12 isotope contains 6.022 × 10²³ atoms. What volume in m³ would be needed to store one mole of cube-shaped children's blocks 2.00 cm long on each side? A)4.8 × 10¹⁸ B)1.2 × 10²² C)6.0 × 10²³ D)1.2 × 10²⁴ E)4.8 × 10²⁴

Accepted Answer

The answer of One mole of the carbon-12 isotope contains...

Quiz 1: Getting Started

John and Linda are arguing about the definition of density. John says the density of an object is proportional to its mass. Linda says the object's mass is proportional to its density and to its volume. Which one, if either, is correct?

Which one of the quantities below has dimensions equal to ?

The quantity with the same units as force times time, Ft, with dimensions MLT−1 is

Which quantity can be converted from the English system to the metric system by the conversion factor ?

The equation for the change of position of a train starting at x = 0 m is given by . The dimensions of b are

A standard exam page is 8.5 inches by 11 inches. An exam that is 2.0 mm thick has a volume of

The term occurs in Bernoulli's equation in Chapter 15, with ρ being the density of a fluid and v its speed. The dimensions of this term are

Spike claims that dimensional analysis shows that the correct expression for change in velocity, , is , where m is mass, t is time, and F is the magnitude of force. Carla says that can't be true because the dimensions of force are . Which one, if either, is correct?

The answer to a question is [[MLT−1]]. The question is "What are the dimensions of

A rectangle has a length of 1.323 m and a width of 4.16 m. Using significant figure rules, what is the area of this rectangle?

The density of an object is defined as

Which of the following quantities has the same dimensions as kinetic energy, ? Note: [[a]] = [[g]] = LT−2; [[h]] = L and [[v]] = LT−1.

Which of the following products of ratios gives the conversion factor to convert miles per hour to meters per second ?

The standard exam page is 8.50 inches by 11.0 inches. Its area in cm2 is

One U.S. fluid gallon contains a volume of 231 cubic inches. How many liters of gasoline would you have to buy in Canada to fill a 14-gallon tank? (Note: 1 L = 103 cm3.)

If each frame of a motion picture film is 35 cm high, and 24 frames go by in a second, estimate how many frames are needed to show a two-hour-long movie.

One number has three significant figures and another number has four significant figures. If these numbers are added, subtracted, multiplied, or divided, which operation can produce the greatest number of significant figures?

If you drove day and night without stopping for one year without exceeding the legal highway speed limit in the United States, the maximum number of miles you could drive would be closest to

Which of the following products of ratios gives the conversion factors to convert meters per second to miles per hour ?

One mole of the carbon-12 isotope contains 6.022 × 1023 atoms. What volume in m3 would be needed to store one mole of cube-shaped children's blocks 2.00 cm long on each side?

The standard exam page is 8.50 inches by 11.0 inches. Its area in cm² is

One U.S. fluid gallon contains a volume of 231 cubic inches. How many liters of gasoline would you have to buy in Canada to fill a 14-gallon tank? (Note: 1 L = 103 cm³.)

One mole of the carbon-12 isotope contains 6.022 × 10²³ atoms. What volume in m³ would be needed to store one mole of cube-shaped children's blocks 2.00 cm long on each side?