Question 1

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: 1L = 10⁺³ cm³. ) A)53 B)21 C)14 D)8.0 E)4.0

Accepted Answer

First, calculate the total volume in cubic inches for a 14-gallon tank: 14 gallons * 231 cubic inches/gallon = 3234 cubic inches. Convert cubic inches to liters knowing 1 liter = 1000 cubic centimeters (cm^3) and 1 inch = 2.54 cm. So, 3234 cubic inches * (2.54 cm/inch)^3 = 3234 * 16.387064 cm^3/inch^3 = 52996.5 cm^3 = 53 liters (approximately).

Question 2

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 3

Which one of the quantities below has dimensions equal to $\left[ \frac { \mathrm { ML } } { \mathrm { T } ^ { 2 } } \right]$ ? A)mv B)mv² C) $\frac { m v ^ { 2 } } { r }$ D)mrv E) $\frac { m v ^ { 2 } } { r ^ { 2 } }$

Accepted Answer

The given string of characters in the question is actually a representation of dimensions of some physical quantity. In this case, it represents dimensions of the quantity 'current'. Therefore, we need to choose an option in which the dimensions of 'current' are present. Option A: Dimensions of mv = [M][L][T]⁻¹, current is not present Option B: Dimensions of mv² = [M][L][T]⁻¹, current is not present Option C: Dimensions of 11ea99f6_d75d_45e2_8bb6_c1c7e6860a86_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11 = [I], dimensions of current are present Option D: Dimensions of mrv = [M][L][T]⁻¹, current is not present Option E: Dimensions of 11ea99f6_d75d_45e3_8bb6_2bcdfd9d829f_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11 = [I], dimensions of current are present Therefore, the correct answer is C.

Question 4

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)8 700.
B)300 000.
C)500 000.
D)1 000 000.
E)32 000 000.

Accepted Answer

In the United States, the maximum highway speed limit is typically around 70-80 miles per hour. Assuming you drive at a constant speed of 70 miles per hour, and there are 24 hours in a day, you would cover a distance of 1,680 miles per day. In one year, which is 365 days, you would cover a distance of approximately 613,200 miles.

However, you would need to factor in rest stops, refueling stops, and other necessary breaks. Assuming you take breaks totalling 8 hours per day, your actual driving time would be 16 hours per day. This would reduce your total distance to approximately 493,920 miles.

Additionally, you would need to consider road closures, detours, and other factors that may prevent you from driving on certain highways. Therefore, it's safest to estimate that the maximum number of miles you could drive without exceeding the legal highway speed limit in the United States in one year is 500,000 miles.

Question 5

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)1 400
B)25 000
C)50 000
D)170 000
E)This cannot be determined without knowing how many reels were used.

Accepted Answer

To show a two hour movie we need to calculate the number of frames shown in 2 hours, which is 2 x 60 x 60 x 24 = 345,600 frames. Therefore, the best choice is D, which is 170,000 frames, the closest answer to our estimation.

Question 6

Which of the following products of ratios gives the conversion factor to convert miles per hour $\left( \frac { \mathrm { mi } } { \mathrm { h } } \right)$ to meters per second $\left( \frac { \mathrm { m } } { \mathrm { s } } \right)$ ?
A) $\frac { 5280 \mathrm { f } } { \mathrm { mi } } \cdot \frac { 12 \mathrm { in } } { \mathrm { f } } \cdot \frac { 1 \mathrm { in } } { 2.54 \mathrm {~cm} } \cdot \frac { 1 \mathrm {~m} } { 100 \mathrm {~cm} } \cdot \frac { 1 \mathrm {~h} } { 3600 \mathrm {~s} }$
B) $\frac { 5280 \mathrm { f } } { \mathrm { mi } } \cdot \frac { 12 \mathrm { in } } { \mathrm { f } } \cdot \frac { 2.54 \mathrm {~cm} } { 1 \mathrm { in } } \cdot \frac { 100 \mathrm {~cm} } { 1 \mathrm {~m} } \cdot \frac { 1 \mathrm {~h} } { 3600 \mathrm {~s} }$
C) $$\frac { 1 \mathrm { mi } } { 5280 \mathrm { f } } \cdot \frac { 1 \mathrm { f } } { 12 \mathrm { in } } \cdot \frac { 1 \mathrm { in } } { 2.54 \mathrm {~cm} } \cdot \frac { 100 \mathrm {~cm} } { 1 \mathrm {~m} } \cdot \frac { 3600 \mathrm {~s} } { 1 \mathrm {~h} }$$
D) $$\frac { 5280 \mathrm { f } } { \mathrm { mi } } \cdot \frac { 12 \mathrm { in } } { \mathrm { f } } \cdot \frac { 2.54 \mathrm {~cm} } { 1 \mathrm { in } } \cdot \frac { 1 \mathrm {~m} } { 100 \mathrm {~cm} } \cdot \frac { 1 \mathrm {~h} } { 3600 \mathrm {~s} }$$
E) $\frac { 5280 \mathrm { f } } { \mathrm { mi } } \cdot \frac { 12 \mathrm { in } } { \mathrm { f } } \cdot \frac { 2.54 \mathrm {~cm} } { 1 \mathrm { in } } \cdot \frac { 1 \mathrm {~m} } { 100 \mathrm {~cm} } \cdot \frac { 3600 \mathrm {~s} } { 1 \mathrm {~h} }$

Accepted Answer

The correct conversion factor involves converting miles to feet, feet to inches, inches to centimeters, centimeters to meters, and hours to seconds. Option D correctly follows these conversions with the correct orientation of units.

Question 7

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 8

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

Density is the amount of mass for each unit of volume. It is expressed in units of mass per unit volume, such as g/cm³ or kg/m³. Option A is incorrect because it defines specific volume, the volume occupied by each unit of mass. Option C is incorrect because weight is a force and not a property of matter. Option D is incorrect because it is not a clear definition of density. Option E is incorrect because it describes Avogadro's number and not density.

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) $\frac { m v ^ { 2 } } { r }$ ?"

Accepted Answer

The answer of The answer to a question is [MLT...

Question 10

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) $\frac { m v ^ { 2 } } { r }$

Accepted Answer

The given dimensions for Ft are: MLTF1F1F1S1^F1F1F10¹ Notice that the dimensions for force are MLT-2 (mass, length, time^-2) and the dimensions for time are T (time). Multiplying these yields MLT-1. Therefore, Ft has dimensions of MLT-1 multiplied by T, resulting in the dimensions MLT^2. The only choice with these same dimensions is A) mv. The dimensions for m are M (mass) and the dimensions for velocity are LT^-1 (length, time^-1), so multiplying these yields MLT^-1, which when multiplied by time T, results in MLT^2, the same dimensions as Ft.

Question 11

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. The volume is 215.9 mm * 279.4 mm * 2.0 mm = 1.2 x 10^5 mm^3.

Question 12

The equation for the change of position of a train starting at x = 0 m is given by $x = \frac { 1 } { 2 } a t ^ { 2 } + b t ^ { 3 }$ .The dimensions of b are A)T ^- ³ B)LT ^- ³ C)LT ^- ² D)LT ^- ¹ E)L ^- ¹T ^- ¹

Accepted Answer

The equation given is: x(t) = b(1 - e^(-0.3t)) The dimensions of x(t) must be length (L). The dimensions of time (t) must be time (T). Therefore, the dimensions of b must be: L / (1 - e^(-0.3t)) Simplifying, we get: L / (1 - e^(-0.3T)) This is best represented by option B: LTF1F1F1S1^-F1F1F10³

Question 13

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...

Question 14

Which of the following products of ratios gives the conversion factors to convert meters per second $\left( \frac { \mathrm { m } } { \mathrm { s } } \right)$ to miles per hour $\left( \frac { \mathrm { mi } } { \mathrm { h } } \right)$ ?
A) $\frac { 5280 \mathrm { f } } { \mathrm { mi } } \cdot \frac { 12 \mathrm { in } } { \mathrm { f } } \cdot \frac { 2.54 \mathrm {~cm} } { 1 \mathrm { in } } \cdot \frac { 100 \mathrm {~cm} } { 1 \mathrm {~m} } \cdot \frac { 3600 \mathrm {~s} } { 1 \mathrm {~h} }$
B) $\frac { 5280 \mathrm { f } } { \mathrm { mi } } \cdot \frac { 12 \mathrm { in } } { \mathrm { f } } \cdot \frac { 1 \mathrm { in } } { 2.54 \mathrm {~cm} } \cdot \frac { 1 \mathrm {~m} } { 100 \mathrm {~cm} } \cdot \frac { 1 \mathrm {~h} } { 3600 \mathrm {~s} }$
C) $\frac { 5280 \mathrm { f } } { \mathrm { mi } } \cdot \frac { 12 \mathrm { in } } { \mathrm { f } } \cdot \frac { 2.54 \mathrm {~cm} } { 1 \mathrm { in } } \cdot \frac { 100 \mathrm {~cm} } { 1 \mathrm {~m} } \cdot \frac { 1 \mathrm {~h} } { 3600 \mathrm {~s} }$
D) $\frac { 1 \mathrm { mi } } { 5280 \mathrm { f } } \cdot \frac { 1 \mathrm { f } } { 12 \mathrm { in } } \cdot \frac { 1 \mathrm { in } } { 2.54 \mathrm {~cm} } \cdot \frac { 100 \mathrm {~cm} } { 1 \mathrm {~m} } \cdot \frac { 3600 \mathrm {~s} } { 1 \mathrm {~h} }$
E) $\frac { 1 \mathrm { mi } } { 5280 \mathrm { f } } \cdot \frac { 1 \mathrm { f } } { 12 \mathrm { in } } \cdot \frac { 1 \mathrm { in } } { 2.54 \mathrm {~cm} } \cdot \frac { 1 \mathrm {~m} } { 100 \mathrm {~cm} } \cdot \frac { 3600 \mathrm {~s} } { 1 \mathrm {~h} }$

Accepted Answer

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

Question 15

Find the average density of a red giant star with a mass of 20 * 10³⁰ kg (approximately 10 solar masses)and a radius of 150 *10⁹ m (equal to the Earth's distance from the sun). A)1.41*10^-⁴ kg/m³ B)0.007 kg/m³ C)1.41 kg/m³ D)710 kg/m³ E)1.41*10 ^- ³ kg/m³

Accepted Answer

The answer of Find the average density of a red...

Question 16

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

Accepted Answer

Kinetic energy is given by 1/2mv^2. The dimensions of kinetic energy are [M][L]^2[T]^-2. Among the given options, only option D (mgh) has the same dimensions as kinetic energy.

Question 17

Which quantity can be converted from the English system to the metric system by the conversion factor $\frac { 5280 \mathrm { f } } { \mathrm { mi } } \cdot \frac { 12 \mathrm { in } } { \mathrm { f } } \cdot \frac { 2.54 \mathrm {~cm} } { 1 \mathrm { in } } \cdot \frac { 1 \mathrm {~m} } { 100 \mathrm {~cm} } \cdot \frac { 1 \mathrm {~h} } { 3600 \mathrm {~s} }$ ?
A)feet per second
B)feet per hour
C)miles per second
D)miles per hour
E)miles per minute

Accepted Answer

The conversion factor provided corresponds to miles per hour. Therefore, the quantity that can be converted from the English system to the metric system by this conversion factor is miles per hour.

Question 18

The term $\frac { 1 } { 2 } \rho v ^ { 2 }$ occurs in Bernoulli's equation in Chapter 15,with$\rho$ 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

The answer of The term \(\frac { 1 } {...

Question 19

Find the average density of a white dwarf star if it has a mass equal to that of the sun (2.0 * 10³⁰ kg)and a radius equal to that of the Earth (6.4*10⁶ m). A)9.0 * 10⁶ kg/m³ B)1.8* 10⁷ kg/m³ C)1.8 * 10⁹ kg/m³ D)3.6 * 10¹⁰ kg/m³ E)9.0 *10⁷ kg/m³

Accepted Answer

The average density is calculated using the formula: density = mass/volume. The volume of a sphere is given by (4/3)πr³. Substituting the given mass and radius, the density is approximately 1.8 × 10⁹ kg/m³.

Question 20

Spike claims that dimensional analysis shows that the correct expression for change in velocity, $\vec { v } _ { f } - \vec { v } _ { i }$ ,is $\vec { v } _ { f } - \vec { v } _ { i } = \frac { m t } { F }$ ,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 $\left[ \frac { \mathrm { ML } } { \mathrm { T } ^ { 2 } } \right]$ .Which one,if either,is correct?
A)Spike,because $[ \vec { v } ] = \left[ \frac { M L } { T } \right]$ .
B)Spike,because $[ \vec { v } ] = \left[ \frac { T ^ { 2 } } { L } \right]$ .
C)Carla,because $[ \vec { v } ] = \left[ \frac { L } { T } \right]$ .
D)Carla,because $[ \overrightarrow { \mathrm { v } } ] = \left[ \frac { \mathrm { L } } { \mathrm { MT } } \right]$ .
E)Spike,because the dimensions of force are $[ \overrightarrow { \mathrm { F } } ] = \left[ \frac { \mathrm { T } ^ { 2 } } { \mathrm { ML } } \right]$ .

Accepted Answer

Carla is correct because the dimensions of velocity are $[ \vec { v } ] = \left[ \frac { L } { T } \right]$, and Spike's expression does not match these dimensions.

Quiz 1: Introduction and Vectors

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: 1L = 10⁺³ cm³. )

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 $\left[ \frac { \mathrm { ML } } { \mathrm { T } ^ { 2 } } \right]$ ?

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:

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.

Which of the following products of ratios gives the conversion factor to convert miles per hour $\left( \frac { \mathrm { mi } } { \mathrm { h } } \right)$ to meters per second $\left( \frac { \mathrm { m } } { \mathrm { s } } \right)$ ?

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?

The density of an object is defined as:

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

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

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

The equation for the change of position of a train starting at x = 0 m is given by $x = \frac { 1 } { 2 } a t ^ { 2 } + b t ^ { 3 }$ .The dimensions of b are

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?

Which of the following products of ratios gives the conversion factors to convert meters per second $\left( \frac { \mathrm { m } } { \mathrm { s } } \right)$ to miles per hour $\left( \frac { \mathrm { mi } } { \mathrm { h } } \right)$ ?

Find the average density of a red giant star with a mass of 20 * 10³⁰ kg (approximately 10 solar masses) and a radius of 150 *10⁹ m (equal to the Earth's distance from the sun) .

Which of the following quantities has the same dimensions as kinetic energy, $\frac { 1 } { 2 } m v ^ { 2 }$ ? Note: [a] = [g] = LT ^- ²;[h] = L and [v] = LT ^- ¹.

The term $\frac { 1 } { 2 } \rho v ^ { 2 }$ occurs in Bernoulli's equation in Chapter 15,with $\rho$ being the density of a fluid and v its speed.The dimensions of this term are

Find the average density of a white dwarf star if it has a mass equal to that of the sun (2.0 * 10³⁰ kg) and a radius equal to that of the Earth (6.4*10⁶ m) .

Quiz 1: Introduction and Vectors

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: 1L = 10+3 cm3. )

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 [MLT2]\left[ \frac { \mathrm { ML } } { \mathrm { T } ^ { 2 } } \right][T2ML​] ?

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:

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.

Which of the following products of ratios gives the conversion factor to convert miles per hour (mih) \left( \frac { \mathrm { mi } } { \mathrm { h } } \right) (hmi​) to meters per second (ms) \left( \frac { \mathrm { m } } { \mathrm { s } } \right) (sm​) ?

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?

The density of an object is defined as:

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

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

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

The equation for the change of position of a train starting at x = 0 m is given by x=12at2+bt3x = \frac { 1 } { 2 } a t ^ { 2 } + b t ^ { 3 }x=21​at2+bt3 .The dimensions of b are

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?

Which of the following products of ratios gives the conversion factors to convert meters per second (ms) \left( \frac { \mathrm { m } } { \mathrm { s } } \right) (sm​) to miles per hour (mih) \left( \frac { \mathrm { mi } } { \mathrm { h } } \right) (hmi​) ?

Find the average density of a red giant star with a mass of 20 * 1030 kg (approximately 10 solar masses) and a radius of 150 *109 m (equal to the Earth's distance from the sun) .

Which of the following quantities has the same dimensions as kinetic energy, 12mv2\frac { 1 } { 2 } m v ^ { 2 }21​mv2 ? Note: [a] = [g] = LT - 2;[h] = L and [v] = LT - 1.

The term 12ρv2\frac { 1 } { 2 } \rho v ^ { 2 }21​ρv2 occurs in Bernoulli's equation in Chapter 15,with ρ\rhoρ being the density of a fluid and v its speed.The dimensions of this term are

Find the average density of a white dwarf star if it has a mass equal to that of the sun (2.0 * 1030 kg) and a radius equal to that of the Earth (6.4*106 m) .