Chapter 1 Introduction Multiple Choice Questions Solutions

According to Newton’s second law, Force = mass × acceleration. Thus, the units of Force must be the product of
the units of mass (kg) and the units of acceleration (m/s2). This yields, kg m/s2, which is answer (a).
2.
Both answers (d) and (e) could be physically meaningful. Answers (a), (b), and (c) must be meaningless since
quantities can be added or subtracted only if they have the same dimensions.
3.
Using a calculator to multiply the length by the width gives a raw answer of 6 783 m2, but this answer must be
rounded to contain the same number of significant figures as the least accurate factor in the product. The least accurate
factor is the length, which contains either 2 or 3 significant figures, depending on whether the trailing zero is
significant or is being used only to locate the decimal point. Assuming the length contains 3 significant figures, answer
(c) correctly expresses the area as 6.78 × 103 m2. However, if the length contains only 2 significant figures,
answer (d) gives the correct result as 6.8 × 103 m2.
4.
The calculator gives an answer of 57.573 for the sum of the 4 given numbers. However, this sum must be rounded
to 58 as given in answer (d) so the number of decimal places in the result is the same (zero) as the number of decimal
places in the integer 15 (the term in the sum containing the smallest number of decimal places).
5.
The required conversion is given by:
This result corresponds to answer (c).
6.
The given area (1 420 ft2) contains 3 significant figures, assuming that the trailing zero is used only to locate the
decimal point. The conversion of this value to square meters is given by:
Note that the result contains 3 significant figures, the same as the number of significant figures in the least accurate
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factor used in the calculation. This result matches answer (c).
7.
The population of the Earth is approximately 6 billion people, including women and children. If we assume the
average person has a mass of about 50 kg (i.e., weighs approximately 110 lbs at Earth’s surface), the total mass of
all the people living on Earth would be on the order of
m ∼ (6 × 109 peoples)(50 kg/person) = 3 × 1011 kg
which agrees with answer (d).
8.
The given Cartesian coordinates are x = −5.00, and y = 12.00, with the least accurate containing 3 significant figures.
Note that the specified point is in the second quadrant. The conversion to polar coordinates is then given by:
Note that 180° was added in the last step to yield a second quadrant angle. The correct answer is therefore (b).
9.
The situation described is shown in the drawing at the right:
From this, observe that , or
h = (45 m)tan 26° = 22 m
Thus, the correct answer is (a).
10.
An adult at rest has a respiration rate that is on the order of 10 breaths/minute. The approximate number of breaths
one would take over a period of 70 years is then
The correct answer is then seen to be (c).
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11.
Doing dimensional analysis on the first 4 given choices yields:
(a)
(b)
(c)
(d)
Since acceleration has units of length divided by time squared, it is seen that the relation given in answer (d) is consistent
with an expression yielding a value for acceleration.