Chapter 1, Introduction
CHAPTER 1
Conceptual Problems
C1. A room in a house has a floor area of 120 ft2. Which of the following is most likely the
approximate volume of the room?
a. 3 m3
b. 30 m3
c. 300 m3
d. 3 000 m3
C2. When SI units are plugged into an equation, it is found that the units balance. Which of the
following can we expect to be true for this equation?
a. The equation will be dimensionally correct.
b. The equation will be dimensionally correct except sometimes in cases when the right
hand side of the equation has more than one term.
c. The equation will not be dimensionally correct.
d. All constants of proportionality will be correct.
C3. How long has it been that scientists have accepted that the nucleus of the atom consists of
neutrons and protons? Think of your answers in terms of order of magnitude.
a. about a decade
b. about a century
c. about a thousand years
d. since Aristotle
C4. Consider the sine of any angle between 30° and 40°. If the angle were doubled, what would
happen to the sine of the angle?
a. It would double.
b. It would more than double.
c. It would increase but be less than double.
d. In different cases, it could do any of the above.
C5. There are other ways of expressing uncertainty besides significant figures. For example,
suppose a quantity is known to have a value between 20.4 and 20.0 and our best estimate of
the value is midrange at 20.2. We could write the number as 20.2 +/- 0.2 and say that the
number has a 1% uncertainty. We would also say it has 3 significant figures. If we square a
number with 1% uncertainty (i.e., 2 parts in about 200) and 3 significant figures, what
results?
a. A number with 1% uncertainty and 3 significant figures.
b. A number with 2% uncertainty and 3 significant figures.
c. A number with 2% uncertainty and 2 significant figures.
d. A number with 1% uncertainty and 2 significant figures.
1
, Chapter 1, Introduction
1.1 Standards of Length, Mass, and Time
1. Since 1983 the standard meter has been defined in terms of which of the following?
a. specific alloy bar housed at Sevres, France
b. wavelength of light emitted by krypton-86
c. distance from the Earth’s equator to the North Pole
d. the distance light travels in a certain fraction of a second
2. Since 1967 the standard definition for the second has been based on which of the following?
a. characteristic frequency of the cesium-133 atom
b. average solar day
c. sidereal day
d. Greenwich Civil Time
3. In mechanics, physicists use three basic quantities to derive additional quantities. Mass is one
of the three quantities. What are the other two?
a. length and force
b. power and force
c. length and time
d. force and time
4. The prefixes which are abbreviated p, n, and G represent which of the following?
a. 10-2, 10-6, and 1015
b. 10-9, 106, and 1010
c. 10-12, 10-9, and 109
d. 10-15, 10-6, and 1012
5. The ratio M/m of the prefixes M and m has what value?
a. 103
b. 106
c. 109
d. 1018
6. One year is about ________ seconds while one day is exactly ________ seconds.
a. 3.16 × 107, 86 400
b. 5.26 × 105, 86 400
c. 3.16 × 107, 8 640
d. 1.04 × 106, 36 000
2
, Chapter 1, Introduction
1.2 The Building Blocks of Matter
7. The nuclei of atoms contain:
a. electrons only.
b. neutrons only.
c. protons and electrons.
d. protons and neutrons.
8. When was the existence of the neutron confirmed?
a. in ancient times
b. in 1895
c. in 1932
d. in 1969
9. The proton contains which of the following combination of quarks?
a. two up quarks and one down quark
b. one up quark and two down quarks
c. one top quark and two bottom quarks
d. two top quarks and one bottom quark
1.3 Dimensional Analysis
10. Which formula is dimensionally consistent with an expression yielding a value for velocity?
(a is acceleration, x is distance, and t is time)
a. v/t2
b. vx2
c. v2/t
d. at
11. Which expression is dimensionally consistent with an expression that would yield a value for
time−1?(v is velocity, x is distance, and t is time)
a. v/x
b. v2/x
c. x/t
d. v2t
3
, Chapter 1, Introduction
12. If the displacement of an object, x, is related to velocity, v, according to the relation x = Av,
the constant, A, has the dimension of which of the following?
a. acceleration
b. length
c. time
d. area
13. The speed of a boat is often given in knots. If a speed of 5 knots were expressed in the SI
system of units, the units would be:
a. m.
b. s.
c. m/s.
d. kg/s.
14. If a is acceleration, v is velocity, x is position, and t is time, then which equation is not
dimensionally correct?
a. t = x/v
b. a = v2/x
c. v = a/t
d. t2 = 2x/a
15. Suppose an equation relating position, x, to time, t, is given by x = b t3 + c t4, where b and c
are constants. The dimensions of b and c are respectively:
a. T3, T4.
b. 1/T3, 1/T4.
c. L/T3, L/T4.
d. L2⋅T3, L2⋅T4.
16. Areas always have dimensions ____ while volumes always have dimensions ____.
a. m2, m3
b. L2, L3
c. Both a and b are correct.
d. No answer is correct because of the “always”.
4
CHAPTER 1
Conceptual Problems
C1. A room in a house has a floor area of 120 ft2. Which of the following is most likely the
approximate volume of the room?
a. 3 m3
b. 30 m3
c. 300 m3
d. 3 000 m3
C2. When SI units are plugged into an equation, it is found that the units balance. Which of the
following can we expect to be true for this equation?
a. The equation will be dimensionally correct.
b. The equation will be dimensionally correct except sometimes in cases when the right
hand side of the equation has more than one term.
c. The equation will not be dimensionally correct.
d. All constants of proportionality will be correct.
C3. How long has it been that scientists have accepted that the nucleus of the atom consists of
neutrons and protons? Think of your answers in terms of order of magnitude.
a. about a decade
b. about a century
c. about a thousand years
d. since Aristotle
C4. Consider the sine of any angle between 30° and 40°. If the angle were doubled, what would
happen to the sine of the angle?
a. It would double.
b. It would more than double.
c. It would increase but be less than double.
d. In different cases, it could do any of the above.
C5. There are other ways of expressing uncertainty besides significant figures. For example,
suppose a quantity is known to have a value between 20.4 and 20.0 and our best estimate of
the value is midrange at 20.2. We could write the number as 20.2 +/- 0.2 and say that the
number has a 1% uncertainty. We would also say it has 3 significant figures. If we square a
number with 1% uncertainty (i.e., 2 parts in about 200) and 3 significant figures, what
results?
a. A number with 1% uncertainty and 3 significant figures.
b. A number with 2% uncertainty and 3 significant figures.
c. A number with 2% uncertainty and 2 significant figures.
d. A number with 1% uncertainty and 2 significant figures.
1
, Chapter 1, Introduction
1.1 Standards of Length, Mass, and Time
1. Since 1983 the standard meter has been defined in terms of which of the following?
a. specific alloy bar housed at Sevres, France
b. wavelength of light emitted by krypton-86
c. distance from the Earth’s equator to the North Pole
d. the distance light travels in a certain fraction of a second
2. Since 1967 the standard definition for the second has been based on which of the following?
a. characteristic frequency of the cesium-133 atom
b. average solar day
c. sidereal day
d. Greenwich Civil Time
3. In mechanics, physicists use three basic quantities to derive additional quantities. Mass is one
of the three quantities. What are the other two?
a. length and force
b. power and force
c. length and time
d. force and time
4. The prefixes which are abbreviated p, n, and G represent which of the following?
a. 10-2, 10-6, and 1015
b. 10-9, 106, and 1010
c. 10-12, 10-9, and 109
d. 10-15, 10-6, and 1012
5. The ratio M/m of the prefixes M and m has what value?
a. 103
b. 106
c. 109
d. 1018
6. One year is about ________ seconds while one day is exactly ________ seconds.
a. 3.16 × 107, 86 400
b. 5.26 × 105, 86 400
c. 3.16 × 107, 8 640
d. 1.04 × 106, 36 000
2
, Chapter 1, Introduction
1.2 The Building Blocks of Matter
7. The nuclei of atoms contain:
a. electrons only.
b. neutrons only.
c. protons and electrons.
d. protons and neutrons.
8. When was the existence of the neutron confirmed?
a. in ancient times
b. in 1895
c. in 1932
d. in 1969
9. The proton contains which of the following combination of quarks?
a. two up quarks and one down quark
b. one up quark and two down quarks
c. one top quark and two bottom quarks
d. two top quarks and one bottom quark
1.3 Dimensional Analysis
10. Which formula is dimensionally consistent with an expression yielding a value for velocity?
(a is acceleration, x is distance, and t is time)
a. v/t2
b. vx2
c. v2/t
d. at
11. Which expression is dimensionally consistent with an expression that would yield a value for
time−1?(v is velocity, x is distance, and t is time)
a. v/x
b. v2/x
c. x/t
d. v2t
3
, Chapter 1, Introduction
12. If the displacement of an object, x, is related to velocity, v, according to the relation x = Av,
the constant, A, has the dimension of which of the following?
a. acceleration
b. length
c. time
d. area
13. The speed of a boat is often given in knots. If a speed of 5 knots were expressed in the SI
system of units, the units would be:
a. m.
b. s.
c. m/s.
d. kg/s.
14. If a is acceleration, v is velocity, x is position, and t is time, then which equation is not
dimensionally correct?
a. t = x/v
b. a = v2/x
c. v = a/t
d. t2 = 2x/a
15. Suppose an equation relating position, x, to time, t, is given by x = b t3 + c t4, where b and c
are constants. The dimensions of b and c are respectively:
a. T3, T4.
b. 1/T3, 1/T4.
c. L/T3, L/T4.
d. L2⋅T3, L2⋅T4.
16. Areas always have dimensions ____ while volumes always have dimensions ____.
a. m2, m3
b. L2, L3
c. Both a and b are correct.
d. No answer is correct because of the “always”.
4
