Introduction

ANSWERS TO MULTIPLE CHOICE QUESTIONS

1. Using a calculator to multiply the length by the width gives a raw answer of 6783 m 2 , 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 × 10 3 m 2 . However, if the length contains only 2 signiﬁcant ﬁgures, answer (d) gives the correct result as 6.8 × 10 3 m 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. 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 s 2 ). This yields kg ⋅ m s 2, which is answer (a). 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). The required conversion is given by: ⎛ 1 000 mm ⎞ ⎛ 1.00 cubitus ⎞ h = ( 2.00 m ) ⎜ ⎟⎜ ⎟ = 4.49 cubiti ⎝ 1.00 m ⎠ ⎝ 445 mm ⎠ This result corresponds to answer (c). 6. The given area (1 420 ft 2 ) 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: 1.00 m ⎞ 2 2 2 A = (1.42 × 10 3 ft 2 ) ⎛ ⎜ ⎟ = 1.32 × 10 m = 132 m ⎝ 3.281 ft ⎠ Note that the result contains 3 signiﬁcant ﬁgures, the same as the number of signiﬁcant ﬁgures in the least accurate factor used in the calculation. This result matches answer (b). 7. You cannot add, subtract, or equate a number apples and a number of days. Thus, the answer is yes for (a), (c), and (e). However, you can multiply or divide a number of apples and a number of days. For example, you might divide the number of apples by a number of days to ﬁnd the number of apples you could eat per day. In summary, the answers are (a) yes, (b) no, (c) yes, (d) no, and (e) yes. 2

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3.

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1 http://helpyoustudy.info

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Chapter 1

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 (with x < 0 and y > 0 ) is in the second quadrant. The conversion to polar coordinates is then given by: r = x 2 + y 2 = ( −5.00 ) + (12.00 ) = 13.0 2 2

tan θ =

y 12.00 = = −2.40 x −5.00

and θ = tan −1 ( −2.40 ) = −67.3° + 180° = 113°

Note that 180° was added in the last step to yield a second quadrant angle. The correct answer is therefore (b) (13.0, 113°). 9. Doing dimensional analysis on the ﬁrst 4 given choices yields: (a)

[ v]

⎡t ⎤ ⎣ ⎦

2

=

LT L = 3 T2 T

(b)

[ v]

⎡x2 ⎤ ⎣ ⎦

=

LT = L−1T −1 L2

(c)

⎡ v 2 ⎤ ( L T )2 L2 T 2 L2 ⎣ ⎦= = = 3 T T T [t ]

(d)

⎡ v 2 ⎤ ( L T )2 L2 T 2 L ⎣ ⎦= = = 2 L L T [ x]

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. 10. The number of gallons of gasoline she can purchase is # gallons = total expenditure 33 Euros ≈ cost per gallon ⎛ Euros ⎞ ⎛ 1 L ⎞ ⎟ ⎜ 1.5 ⎟⎜ L ⎠ ⎜ 1 quart ⎟ ⎝ ⎝ ⎠ ≈ 5 gal

⎛ 4 quarts ⎜ ⎜ 1 gal ⎝

⎞ ⎟ ⎟ ⎠

so the correct answer is (b). 11. The situation described is shown in the drawing at the right. h From this, observe that tan 26° = , or 45 m h = ( 45 m ) tan 26° = 22 m 26

h

Thus, the correct answer is (a). 12.

45 m

Note that we may write 1.365 248 0 × 10 7 as...