Question 1

You measure the height of a building using your knowledge of trigonometry, by measuring the angle to the top of the building from a point on the ground 100.0 m away.  You measure an angle θ=20.0°±1.0°. How high is the building?

Accepted Answer

A)  36.4±1.0 m
B)  36.4±2.0 m
C)  36.4±0.5 m
D)  36.4±3.0 m
E)  36.4±3.6 m B

Question 2

A 2.00 m by 3.00 m plate of aluminium has a mass of 324 kg. What is the thickness of the plate? (The density of aluminium is 2.70 *103 kg/m3.)

Accepted Answer

2.00 cm

Question 3

At the end of a year, a motor car company announces that sales of a pickup are down 43% for the year. If sales continue to decrease by 43% in each succeeding year, how long will it take for sales to decrease to zero?

Accepted Answer

A)  1 year
B)  2 years
C)  3 years
D)  4 years
E)  More than 4 years E

Question 4

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

Accepted Answer

A)  mr?'
B)  mvr?'
C)  ma?'
D)  mat?'
E)    mv2r\frac{m v^{2}}{r}rmv2​  ?'

Question 5

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:

Accepted Answer

A)  T-3
B)  LT-3
C)  LT-2
D)  LT-1
E)  L-1T-1

Question 6

When doing a physics problem, you were asked to calculate how fast a car was going in a particular situation. You came up with an answer of 230 m/s. You want to check if this is plausible, by converting this number into more familiar units: kilometres per hour. What is 230 m/s when converted into kilometres per hour, and is this a plausible speed for a car?

Accepted Answer

A)  230 km/hr: not plausible
B)  828 km/hr: not plausible
C)  64 km/hr: plausible
D)  2.3 km/hr: plausible
E)  23 km/hr: plausible

Question 7

What is the mass of air in a room that measures 5.0 m * 8.0 m *3.0 m? (The density of air is 1/800 that of water).

Accepted Answer

The answer of What is the mass of air in...

Question 8

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

Accepted Answer

A)  mv
B)  mvr
C)  mv2r
D)  ma
E)    mv2r\frac{m v^{2}}{r}rmv2​

Question 9

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.

Accepted Answer

A)  ma
B)  mvx
C)  mvt
D)  mgh
E)  mgt

Question 10

A standard exam page is 210 mm by 297 mm. An exam that is 2.0 mm thick has a volume of:

Accepted Answer

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.

Question 11

You are trying to compare the fuel efficiency of two cars, one made in the US and one made in Australia. You know that the Australian car will use 14 litres of fuel per 100 km of driving. The US car has been tested as getting 10 miles per gallon of fuel used. A mile is 1.609 km and a US gallon is 3.785 litres. How many litres will the US car use per 100 km of driving?

Accepted Answer

A)  23.5
B)  14.5
C)  14.0
D)  13.2
E)  10.0

Question 12

Which one of the quantities below has dimensions equal to $\left[\frac{\mathrm{ML}}{\mathrm{~T}^{2}}\right]$ ?

Accepted Answer

A)  mv
B)  mv2
C)    mv2r\frac{m v^{2}}{r}rmv2​ 
D)  mrv
E)    mv2r2\frac{m v^{2}}{r^{2}}r2mv2​

Question 13

The term $\frac{1}{2} \rho \nu^{2}$ 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:

Accepted Answer

A)  M-1L5T2
B)  MLT2
C)  ML-1T-2
D)  M-1L9T-2
E)  M-1L3T-2

Question 14

Five people measure the length of a car. The values they obtain are 2.38 m, 2.36 m, 2.41 m, 2.36 m and 2.37 m. What is the approximate uncertainty in their measurement of the length of the car?

Accepted Answer

A)  5 cm
B)  1 m
C)  1 cm
D)  0.01 cm
E)  0.5 cm

Question 15

Two rocket engineers are trying to see whether a changed nozzle design makes their rockets go faster. The first rocket travels at a speed of 1000±3 m/s, while the second rocket travels at a speed of 1005±2 m/s. How much faster is the second rocket?

Accepted Answer

A)  5±2 m/s
B)  5±3 m/s
C)  5±4 m/s
D)  5±5 m/s
E)  5±6 m/s

Question 16

Which of the following products of ratios gives the conversion factors to convert metres per second $\left(\frac{\mathrm{m}}{\mathrm{~s}}\right)$ to parsecs per year $\left(\frac{\text { Parsec }}{\text { Year }}\right)$ ? A parsec is a unit of distance used in astrophysics, and is equal to 3.26 light years. A light year is 9.46 x 1015 m.

Accepted Answer

A)    1 parsec 3.26 light years 1 light year 9.46×1015m365 days 1 year 24 hours 1 day 3600 s1 hour \frac{1 	ext { parsec }}{3.26 	ext { light years }} \frac{1 	ext { light year }}{9.46 	imes 10^{15} m} \frac{365 	ext { days }}{1 	ext { year }} \frac{24 	ext { hours }}{1 	ext { day }} \frac{3600 \mathrm{~s}}{1 	ext { hour }}3.26 light years 1 parsec ​9.46×1015m1 light year ​1 year 365 days ​1 day 24 hours ​1 hour 3600 s​ 
B)    1 parsec 3.26 light years 1 light year 9.46×1015m365 days 1 year 3600 s1 hour \frac{1 	ext { parsec }}{3.26 	ext { light years }} \frac{1 	ext { light year }}{9.46 	imes 10^{15} m} \frac{365 	ext { days }}{1 	ext { year }} \frac{3600 \mathrm{~s}}{1 	ext { hour }}3.26 light years 1 parsec ​9.46×1015m1 light year ​1 year 365 days ​1 hour 3600 s​ 
C)   
D)    1 parsec 3.26 light years 1 light year 9.46×1015m1 hour 3600 s24 hours 1 day 1 year 365 days \frac{1 	ext { parsec }}{3.26 	ext { light years }} \frac{1 	ext { light year }}{9.46 	imes 10^{15} m} \frac{1 	ext { hour }}{3600 \mathrm{~s}} \frac{24 	ext { hours }}{1 	ext { day }} \frac{1 	ext { year }}{365 	ext { days }}3.26 light years 1 parsec ​9.46×1015m1 light year ​3600 s1 hour ​1 day 24 hours ​365 days 1 year ​ 
E)    1 parsec 3.26 light years 1 light year 9.46×1015m365 days 1 year 24 hours 1 day 60 s1 hour \frac{1 	ext { parsec }}{3.26 	ext { light years }} \frac{1 	ext { light year }}{9.46 	imes 10^{15} m} \frac{365 	ext { days }}{1 	ext { year }} \frac{24 	ext { hours }}{1 	ext { day }} \frac{60 \mathrm{~s}}{1 	ext { hour }}3.26 light years 1 parsec ​9.46×1015m1 light year ​1 year 365 days ​1 day 24 hours ​1 hour 60 s​

Question 17

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?

Accepted Answer

A)  the addition
B)  the subtraction
C)  the multiplication
D)  the division
E)  All the operations result in the same number of significant figures.

Question 18

Spike claims that dimensional analysis shows that the correct expression for change in velocity is $\vec{v}_{f}-\vec{v}_{i}$ , is $\overrightarrow{\mathrm{v}}_{f}-\overrightarrow{\mathrm{v}}_{i}=\frac{m t}{F}$ , 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?

Accepted Answer

A)  Spike, because  [v→]=[ML T][\overrightarrow{\mathrm{v}}]=\left[\frac{\mathrm{ML}}{\mathrm{~T}}\right][v-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"/>]=[ TML​]  .
B)  Spike, because  [v→]=[T2 L][\overrightarrow{\mathrm{v}}]=\left[\frac{\mathrm{T}^{2}}{\mathrm{~L}}\right][v-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"/>]=[ LT2​]  .
C)  Carla, because  [v→]=[L T][\overrightarrow{\mathrm{v}}]=\left[\frac{\mathrm{L}}{\mathrm{~T}}\right][v-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"/>]=[ TL​]  .
D)  Carla, because  [V→]=[LMT][\overrightarrow{\mathrm{V}}]=\left[\frac{\mathrm{L}}{\mathrm{MT}}\right][V-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"/>]=[MTL​]  .
E)  Spike, because the dimensions of force are  [F→]=[T2ML][\overrightarrow{\mathrm{F}}]=\left[\frac{\mathrm{T}^{2}}{\mathrm{ML}}\right][F-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"/>]=[MLT2​]  .

Question 19

A rectangle has a length of 1.323 m and a width of 4.16 m. Using significant figure rules, what is the area of this rectangle?

Accepted Answer

A)  5.503 68 m2
B)  5.503 7 m2
C)  5.504 m2
D)  5.50 m2
E)  5.5 m2

Question 20

The density of an object is defined as:

Accepted Answer

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.

Exam 1: Physics and Measurement

You measure the height of a building using your knowledge of trigonometry, by measuring the angle to the top of the building from a point on the ground 100.0 m away. You measure an angle θ=20.0°±1.0°. How high is the building?