College Physics: Multiple Choice Questions
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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
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