physical quantities - hiroshmendis.com

Physical Quantities

Cambridge Ordinary level

Physics 5054

Unit 1.1

Cambridge Assessment International Education

Cambridge Ordinary Level

Grade 9

Unit 1.1

Physics 5054

Theory

Physical Quantities

Hirosh Mendi s

New syllabus

First print 2021

Science Academy 0 7 7 7 8 7 6 9 8 1

w w w . h i r o s h m e n d i s . c o m

Contents

Syllabus ........................................ 5

Motion, forces and energy ............... 5

Physical quantities and measurement

techniques ................................ 5

Units and Quantities ......................... 6

Fundamental Quantities .................. 6

Derived Quantities ......................... 6

Numbers .................................... 7

Prefix ...................................... 7

Scientific notation ....................... 7

Significant figures ....................... 7

Measuring techniques ........................ 9

Measuring Length .......................... 9

Trundle wheel ............................ 9

Measuring tape .......................... 9

Meter rule ................................. 9

Vernier calipers .......................... 9

Parts of Vernier Calipers ............ 10

Micrometer ............................... 10

Errors and improvements ........... 11

Measuring Volume ........................ 11

Measuring Time ........................... 12

Scalars and Vectors ......................... 13

Addition or composition of vectors ..... 13

Vectors acting same direction ..... 13

Vectors acting opposite direction . 13

Vectors acting perpendicular to each

other ................................... 14

Vectors acting at any other angles to

each other ............................. 14

Triangle low of vectors / Vector

triangle .............................. 14

Power parallelogram .............. 14

Questions ..................................... 15

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Syllabus

Motion, forces and energy

Physical quantities and measurement techniques

1. Describe how to measure a variety of lengths with appropriate precision using tapes, rulers and micrometers (including reading the scale on an analogue micrometer)

2. Describe how to use a measuring cylinder to measure the volume of a liquid and to determine the volume of a solid by displacement

3. Describe how to measure a variety of time intervals using clocks and digital timers 4. Determine an average value for a small distance and for a short interval of time by measuring

multiples (including the period of oscillation of a pendulum) 5. Understand that a scalar quantity has magnitude (size) only and that a vector quantity has

magnitude and direction 6. Know that the following quantities are scalars: distance, speed, time, mass, energy and temperature 7. Know that the following quantities are vectors: displacement, force, weight, velocity, acceleration,

momentum, electric field strength and gravitational field strength 8. Determine, by calculation or graphically, the resultant of two vectors at right angles


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Units and Quantities

Fundamental Quantities

The basic step of most scientific research is obtaining measurements. There are several hundreds of quantities to measure but, the Système Internationale d’Unités (SI) or

International System of Units, defines seven units of measure as a basic set from which all other SI units are derived.

These SI base units and their physical quantities are: Base quantity SI base unit

Instrument Name Symbol Name Symbol

length l meter m ruler, tape

mass m kilogram kg scale, balance

time t second s stop watch

electric current I Ampere A ammeter

temperature T Kelvin K thermometer

amount of substance n mole mol

luminous intensity Iv candela cd light meter

Derived Quantities

All other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations.

Derived quantity Unit

Name Symbol Name Symbol

area A square meter m2

volume V cubic meter m3

speed, velocity v meter per second m/s

acceleration a meter per second squared m/s2

density ρ kilogram per cubic meter kg/m3

For ease of understanding and convenience, some derived units have been given special names and symbols.

Derived

quantity Name Symbol

Expression in terms

of other SI units

Expression in terms

of SI base units

frequency Hertz Hz - s-1

force Newton N - m kg s-2

pressure Pascal Pa N/m2 m-1 kg s-2

energy, work Joule J N m m2 kg s-2

power Watt W J/s m2 kg s-3

resistance Ohm Ω V/A m2 kg s-3 A-2

voltage Volt V W/A m2 kg s-3 A-1



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Numbers

Prefix

Magnitudes of some physical quantities are too big or too small numbers, which are inconvenient to handle.

Without changing the value, a prefix is added in front of the unit to change the number to an appropriate one.

Some of the mostly applicable prefixes are... Prefix Symbol 10n Decimal Name

tera T 1012 1 000 000 000 000 trillion

giga G 109 1 000 000 000 billion

mega M 106 1 000 000 million

kilo k 103 1 000 thousand

hecto h 102 100 hundred

deca da 101 10 ten

100 1 one

deci d 10-1 0.1 tenth

centi c 10-2 0.01 hundredth

mili m 10-3 0.001 thousandth

micro μ 10-6 0.000 001 millionth

nano n 10-9 0.000 000 001 billionth

pico p 10-12 0.000 000 000 001 trillionth

The number 10100 is called googol, the famous web browser Google got their name by deriving the googol.

Scientific notation

Scientific notation is a way of writing numbers that are too big or too small to be conveniently written in decimal form.

When a number is converted into scientific notation, it is scaled down to a number between 1 and 10. All the significant digits remain, but all of the places holding zeroes are incorporated into the exponent. Following these rules, 1,230,400 becomes 1.2304 × 106.

Significant figures

Every measurement of a quantity is an attempt to find its true value and is subject to errors arising from limitations of the apparatus and the experimenter.

The number of figures, called significant figures, given for a measurement indicates how accurate we think it is and more figures should not be given than is justified.

For example, a value of 4.5 for a measurement has two significant figures; 0.0385 has three significant figures, 3 being the most significant and 5 the least, i.e. it is the one we are least sure about since it might be 4 or it might be 6. Perhaps it had to be estimated by the experimenter because the reading was between two marks on a scale.



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When doing a calculation answer should have the same number of significant figures as the measurements used in the calculation.

For example, if the calculator gave an answer of 3.4185062, this would be written as 3.4 if the measurements had two significant figures.

It would be written as 3.42 for three significant figures. Note that in deciding the least significant figure you look at the next figure to the right. If it is less than 5 you leave the least significant figure as it is (hence 3.41 becomes 3.4) but if it equals or

is greater than 5 you increase the least significant figure by 1 (hence 3.418 becomes 3.42). If a number is expressed in standard notation, the number of significant figures is the number of digits

before the power of ten. For example, 2.73 × 103 has three significant figures.



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Measuring techniques

Measuring Length

Length can be measured using a trundle wheel, measuring tape, rule, vernier caliper or micrometer screw gauge.

Trundle wheel

The trundle wheel is composed of a wheel of fixed circumference, a handle which is attached to the axle allowing the trundle wheel to be held easily, and a clicking device which is triggered once per revolution of the wheel.

Trundle wheels are not as accurate as other methods of measuring distance but are a good way to get a rough estimation of a fairly long distance over a good surface.

Smallest reading – 1 cm, no limitation for maximum reading.

Measuring tape

A tape measure or measuring tape is a flexible ruler and used to measure distance.

It consists of a ribbon of cloth, plastic, fibre glass, or metal strip with linear-measurement markings.

Used to measure the lengths more than a metre or curved surfaces.

Smallest reading – 1 cm or 1 mm, largest reading is 50 m or 100 m.

Meter rule

Used to measure the lengths less than a metre. If the given quantity to be measure is more than a metre two

rules should be used. Smallest reading – 1 cm or 1 mm, largest reading is 1 m.

Vernier calipers

The Vernier caliper is an extremely accurate measuring instrument; the uncertainty is 1/20 mm = 0.05 mm.



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Parts of Vernier Calipers

Main Scale: It is a simple ruler made of metal. The numbers on the fixed scale are centimeters. The tick marks on the fixed scale between the numbers are millimeters.

Vernier Scale: It is similar to a normal scale, but it has divisions which are different from the common 1 mm. usually 9mm divided to 10 subdivisions.

Inside Jaws: They are used to measure the internal features of an object such as the internal diameter of a hollow cylinder. One of these is fixed while the other is movable.

Outside jaws: They are used for normal measurements of lengths of various objects. One of these is fixed while the other is movable.

Depth Probe: It is a metal depth that is used for measuring depths, such as the depth of a cylinder. Screw: It is used to fix the length between the jaws once the measurement of the object has been taken

by the jaws. Smallest reading – 0.1 mm, largest reading is 15 cm.

Micrometer

The micrometer is an accurate measuring instrument. Each revolution of the rachet moves the spindle face 0.5mm towards the anvil face. The object to be measured is placed between the anvil face and the spindle face. The rachet is turned clockwise until the object is ‘trapped’ between these two surfaces and the rachet

makes a ‘clicking’ noise.

This means that the rachet cannot be tightened anymore and the measurement can be read. Smallest reading – 0.01 mm, largest reading is 5 cm.



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Errors and improvements

The reading is 76 mm or 7.6 cm. The eye must be directly over the mark on the scale or the thickness of the ruler causes a parallax error.

To obtain more accurate value for a small distance, multiples can be measured. For example, instead of one CD, measure the thickness of ten CDs, then divide by 10 to obtain the average wavelength.

Measuring Volume

Volume is the amount of space occupied. The unit of volume is the cubic metre (m3) but as this is rather large, for most purposes the cubic

centimetre (cm3) is used. 1 m3 = 1 000 000 cm3

For a regularly shaped object such as a cuboid, volume = length × breadth × height

The volume of a sphere of radius r is 4/3 πr3 and that of a cylinder of radius r and height h is πr2h. The volume of a liquid may be obtained by pouring it

into a measuring cylinder. A known volume can be run off accurately from a

burette. When making a reading both vessels must be upright

and your eye must be level with the bottom of the curved liquid surface, i.e. the meniscus.

The meniscus formed by mercury is curved oppositely to that of other liquids and the top is read.

Liquid volumes are also expressed in litres (l); 1 l = 1000 cm3 = 1 dm3.

1 ml = 1 cm3.

Irregular solid – if the shape is two difficult for the volume to be calculated, the solid can be lowered into a partly filled measuring cylinder.

The rise in level on the volume scale give us the volume of the solid. If the solid floors it can be weighed down with a lump of metal. The total volume is found. The volume of the metal is measured in a separate experiment and then subtract from this total. Using a displacement can – if the solid is too big for a measuring cylinder, its volume can be found

using displacement can. First the can filled up to the level of the spout. Then the solid is slowly lowered into the water.



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The solid has displayed its own volume of water. The displaced water is collected in a measuring cylinder. The displacement method so the story goes was discovered by accident by Archimedes.

Measuring Time

The unit of time is the second (s). Time intervals of many seconds or minutes can be measured using a stop clock or stopwatch. The second is defined as the time interval for a certain number of energy changes to occur in the

caesium atom. To measure very short time intervals, a digital clock that can be triggered to start and stop by an

electronic signal from a microphone, photogate or mechanical switch is useful. Tickertape timers or dataloggers are often used to record short time intervals in motion experiments. Accuracy can be improved by measuring longer time intervals. Several oscillations (rather than just one) are timed to find the period of a pendulum.



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Scalars and Vectors

Scalars are quantities that are fully described by a magnitude (or numerical value) alone. Length, distance, area, volume, speed, mass, density, time, pressure, temperature, energy, work, power

are some scalars. Vectors are quantities that are fully described by both a magnitude and a direction. Displacement, velocity, acceleration, momentum, force, lift, drag, thrust, weight, electric field strength

and gravitational field strength are some vectors. Direction is not concern while adding scalars: - an object traveled 3m forward and then 4m backward,

the total distance traveled is 3 + 4 = 7m. But addition of vectors should be done with directions: - an object traveled 4m forward and then 3m

backward, the total displacement traveled is (+4) + (-3) = (+1)m. (+) means the forward and (-) means the backward.

Addition or composition of vectors

When two or more vectors added, we get a single vector called resultant vector

Vectors acting same direction

Vectors acting opposite direction



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Vectors acting perpendicular to each other

Vectors acting at any other angles to each other

Triangle low of vectors / Vector triangle

Power parallelogram



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Questions

1. Forces of 3 N and 4 N act as shown in the diagram.

Which diagram shows the resultant R of these two forces?

2. A micrometer is used to measure the diameter of a uniform wire.

What is done to obtain an accurate answer? A Find the reading and add or subtract the zero error. B Make the micrometer horizontal. C Subtract the fixed scale reading from the rotating scale reading. D Subtract the rotating scale reading from the fixed scale reading.

3. Before marking the finishing line on a running track, a groundsman measures out its 100m length. Which instrument is the most appropriate for this purpose? A measuring tape B metre rule

C 30cm ruler D micrometer



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4. When there is no wind, the engines of an airship push it due north at 20m/ s. The wind is blowing from the west at 12m/ s. Which vector diagram correctly shows how the resultant velocity R of the airship is obtained?

5. A length of copper pipe, of uniform cross-section and several metres long, carries water to a tap.

Measurements are taken to determine accurately the volume of copper in the pipe. Which instruments are used? A calipers and micrometer B micrometer and rule C rule and tape D tape and calipers

6. A workman measures, as accurately as possible, the length and internal diameter of a straight copper pipe. The length is approximately 600 cm and the internal diameter is approximately 2 cm. What is the best combination of instruments for the workman to use?

internal diameter length A ruler ruler B ruler tape C vernier calipers ruler D vernier calipers tape

7. The diagram shows a stopwatch. What is the reading on the stopwatch? A 30.6s B 33.0s

C 36.0s D 36.6s



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8. Each row contains a vector and a scalar.

In which row is the size of the vector equal to the size of the scalar? vector scalar

A displacement of a car speed of the car B B velocity of a car distance travelled by the car C velocity of a car speed of the car D weight of a car mass of the car

9. What is the size of the resultant of the two forces shown in the diagram? A 1.0N B 3.5N

C 5.0N D 7.0N

10. A student measures, as accurately as possible, the length and internal diameter of a straight glass tube.

The length is approximately 25 cm and the internal diameter is approximately 2 cm. What is the best combination of instruments for the student to use?

internal diameter length A ruler micrometer B ruler ruler C vernier calipers micrometer D vernier calipers ruler

11. Forces of 25N and 40N act on an object in the directions shown.

Which arrow shows the direction of the resultant force on the object?

12. Which device can be used to measure the thickness of a single sheet of paper? A a metre rule B a micrometer

C a plastic ruler D a measuring tape



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13. Which quantity is a scalar? A acceleration B force C temperature D velocity

14. The diameter and the length of a thin wire, approximately 50 cm in length, are measured as precisely

as possible. What are the best instruments to use? diameter length

A micrometer rule B micrometer vernier calipers C rule tape D vernier calipers rule

15. Is mass a scalar or a vector, and is acceleration a scalar or a vector?

mass acceleration A scalar scalar B scalar vector C vector scalar D vector vector

16. During an experiment to find the density of a stone, the stone is lowered into a measuring cylinder

partly filled with water.

Which statement is correct? A The difference between the readings gives the density of the stone. B The difference between the readings gives the volume of the stone. C The final reading gives the density of the stone. D The final reading gives the volume of the stone.

17. The diagram shows a micrometer scale.

Which reading is shown? A 5.64mm B 7.14mm C 7.16mm D 7.64mm



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18. Which is a scalar quantity? A mass B force C velocity D weight

19. The diagram shows arrows representing two vector quantities.

Which diagram shows the resultant R of these two vectors?

20. Which set of quantities are all vectors? A acceleration, displacement, velocity B chemical energy, mass, power C extension, force, gravitational potential energy D weight, kinetic energy, work

21. A student determines the circumference of a golf ball. Which instrument gives a reading that is the circumference of the golf ball? A calipers B micrometer C rule D tape

22. A length of copper wire is labelled ‘length 30 m’ and ‘diameter 0.50 mm’. Which instruments are most suitable to measure accurately the length and the diameter of the wire?

length diameter A rule calipers B rule micrometer C tape calipers D tape micrometer



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23. A car’s acceleration and maximum speed are improved by using an engine of smaller mass and greater driving force. How many of the underlined quantities are vectors? A 1 B 2 C 3 D 4

24. The diagram shows the resultant R of a 3.0 N force and a 4.0 N force acting at a point The angle between the 3.0N force and the 4.0N force can be any value from 0° to 90°. Which value of R is not possible? A 4.0N B 5.0N C 6.0N D 7.0N

25. A car accelerates at 5.0m/ s2 along a straight, horizontal road and reaches a velocity of 20m/ s in a time of 4.0s. During this time, its total displacement is 40m. Which quantity is a scalar? A a displacement of 40m B a time of 4.0s C a velocity of 20m/ s D an acceleration of 5.0m/ s2

26. Which list contains only scalar quantities? A acceleration, displacement, velocity B distance, force, speed C force, length, time D length, mass, speed

27. A manufacturer measures the three dimensions of a wooden floor tile using three different instruments. The approximate dimensions of the tile are shown.

28. Which instruments are used to measure accurately each of these dimensions?

length thickness width A metre rule micrometer calipers B metre rule calipers micrometer C micrometer metre rule calipers D calipers micrometer metre rule



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29. A student wishes to measure directly the circumference of a football. Which is the most suitable instrument to use? A calipers B a measuring tape C a micrometer D a ruler

30. Which is a vector quantity? A a mass of 2.0 kg B a temperature of –10 °C C a weight of 15N D an average speed of 20m / s

31. Forces of 4.0 N and 2.0N act at a point. Which scale diagram shows the forces that have a resultant of 4.0N?

32. What is the name and value of the unit of power written as mW? name value

A megawatt 10–3W B megawatt 106W C milliwatt 10–3W D milliwatt 106W

33. Micrometers, metre rules, tapes and calipers are used for measuring lengths. Which row identifies the most suitable device for accurately measuring the stated length?

length measuring device A 0.15 mm micrometer B 0.50 mm metre rule C 0.15 m tape D 0.50 m calipers



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34. Two forces X and Y act as shown.

Which diagram shows the resultant force R of X and Y?

35. A small cylinder is rolled along a ruler and completes two revolutions.

The circumference is the distance around the outside of a circle. What is the circumference of the cylinder? A 4.4 cm B 5.2 cm C 8.8 cm D 10.2 cm

36. Which quantities are both vectors? A acceleration and length B distance and velocity C length and distance D velocity and acceleration



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37. What is a possible mass for a normal adult person? A 7.5 kg B 75 kg C 750 kg D 7500 kg

38. Which reading is given to one tenth of a millimetre? A 3.3 cm B 3.31 cm C 3.310 cm D 3.312 cm

39. The magnitudes of three different electric charges are given below. What is the correct order of size, from largest to smallest? A 1 mC → 1 MC → 1 kC B 1 MC → 1 mC → 1 kC C 1 MC → 1 kC → 1 mC D 1 kC → 1 mC → 1 MC

40. Which word is the name of a scalar quantity? A acceleration B force C mass D velocity

41. Which word is the name of a vector quantity? A density B displacement C energy D speed

42. What is measured using a micrometer? A area B current C length D mass

43. Stop-watches are used to time the runners in a race. The stop-watches show the times recorded for the winner and another runner.

What is the difference in time between the winner and the other runner? A 0.4608 s B 6.08 s C 46.08 s D 608 s

44. Which diagram shows the vector addition of a 4.0N force and a 3.0N force?



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45. A heavy nail is fixed firmly to a wall. It is pulled by a string at 40 to the vertical. The nail does not move. Three forces act on the nail:

its weight W, the tension T in the string, the force R exerted by the wall.

Which diagram, drawn to scale, represents the three forces?

46. Which quantity is a vector? A acceleration B distance C speed D time

47. A plumber needs to measure the internal diameter of a water pipe as accurately as possible. Which instrument should be used? A measuring tape B metre rule C micrometer D vernier calipers

48. The diagram shows part of a vernier scale.

What is the reading on the vernier scale? A 6.50 cm B 6.55 cm C 7.00 cm D 7.45 cm



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49. One oscillation of a swinging pendulum occurs when the bob moves from X to Y and back to X again.

Using a stopwatch, which would be the most accurate way to measure the time for one oscillation of the pendulum? A Time 20 oscillations and multiply by 20. B Time 20 oscillations and divide by 20. C Time one oscillation. D Time the motion from X to Y, and double it.

50. A student has been asked to determine, as accurately as possible, the volume of a piece of wire. The wire is about 80cm long and about 0.2cm in diameter. Which measuring instruments should the student use?

length diameter A metre rule micrometer B metre rule vernier callipers C micrometer vernier callipers D vernier callipers micrometer

51. The diagram shows part of a vernier scale.

What is the correct reading? A 30.5mm B 33.5mm C 38.0mm D 42.5mm

52. The diagram shows a vernier V placed against a scale S.

What is the vernier reading? A 2.23 B 2.26 C 2.33 D 2.36



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53. Which instrument is used to measure the internal diameter of a pipe with a single measurement? A manometer B measuring cylinder C micrometer D vernier calipers

54. The diagram shows one method of measuring the diameter of a beaker.

What is the diameter of the beaker? A 4.5cm B 5.0cm C 5.5cm D 8.0cm

55. A student studies some equations. power = work / time force = mass × acceleration velocity = displacement/ time

How many vector quantities are contained in the equations? A 1 B 2 C 3 D 4

56. The width of a wooden block is measured using vernier calipers. What is the width of the block? A 3.5mm B 5.3mm

C 8.0mm D 8.5 mm

57. Which of the following correctly lists one scalar and one vector quantity? scalar quantity vector quantity

A displacement work B energy force C force acceleration D velocity mass



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58. In an experiment, a ball is rolled down a curved track that is about half a metre long.

Which measuring device should be used to measure the length accurately? A metre rule B micrometer C tape measure D vernier calipers

59. What is the reading on this micrometer?

A 5.43mm B 6.63mm C 7.30mm D 8.13mm

60. A manufacturer needs to measure accurately the dimensions of a wooden floor tile. The approximate dimensions of the tile are shown.

Which instruments measure each of these dimensions accurately?

length thickness width A metre rule micrometer vernier calipers B metre rule vernier calipers micrometer C micrometer metre rule vernier calipers D vernier calipers micrometer metre rule

61. Two forces F1 and F2 act on an object O in the directions shown.

What is the direction of the resultant force?



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62. Forces of 30N and 50N act on the same body, but in different directions. Which value could not be the

resultant force on the body? A 10N B 30N C 50N D 70N

63. Which statement about scalars and vectors is correct? A A scalar has direction but no size. B A scalar has size but no direction. C A vector has direction but no size. D A vector has size but no direction.

64. Vernier calipers read to one tenth of a millimetre. Which reading shows this precision? A 3.3 cm B 3.31 cm C 3.310 cm D 3.312 cm

65. Which list contains only scalar quantities?

A acceleration, displacement, mass B acceleration, distance, speed C displacement, mass, velocity D distance, mass, speed

66. Power is measured in watts. What is the correct symbol for millions of watts? A mw B mW C Mw D MW

67. The following statements are about motion.

1 A plane flies due East for 600km. 2 A runner’s average speed in a race around a track is 5m/ s. 3 A snail crawls at 3mm/ s in a straight line towards a lettuce. 4 A tourist travels 500km on a journey.

Which statements describe vector quantities? A 1 and 2 B 1 and 3 C 2 and 3 D 2 and 4

68. Vernier calipers are shown with the jaws closed. What is the zero error? A 0.04cm B 0.05cm C 0.14cm D 0.15cm



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69. Which list contains only scalar quantities? A acceleration, displacement, velocity B distance, force, speed C force, length, time D length, mass, speed

70. A plumber measures, as accurately as possible, the length and internal diameter of a straight copper pipe. The length is approximately 80cm and the internal diameter is approximately 2cm. What is the best combination of instruments for the plumber to use?

internal diameter length A rule rule B rule tape C vernier calipers rule D vernier calipers tape

71. A quantity is quoted as having a value of 6.2ms. In what units is it measured?

A metres B metres per second C microseconds D milliseconds

72. Velocity is given by the change in displacement divided by the change in time. How many vector quantities appear in this statement? A 0 B 1 C 2 D 3

73. A micrometer is used to measure the diameter of a uniform wire.

What is done to obtain an accurate answer? A Make the micrometer horizontal and then use the scales to find the reading. B Subtract the fixed-scale reading from the rotating-scale reading. C Subtract the rotating-scale reading from the fixed-scale reading. D Use the scales to find the reading and add or subtract any zero error.



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74. A student uses a measuring cylinder to measure the volume of some water. The diagram shows part of the measuring cylinder. The top and bottom of the meniscus are labelled. What is the volume of the water? A 47.0cm3 B 47.5cm3 C 49.0cm3 D 49.5cm3

75. A student wishes to find the volume of a small, irregularly-shaped stone. A ruler and a measuring cylinder containing some water are available. Which apparatus is needed? A neither the ruler nor the measuring cylinder B the measuring cylinder only C the ruler and the measuring cylinder D the ruler only

76. The diagram shows the height of a stack of identical coins. What is the thickness of one coin? A 0.20mm B 2.0mm C 0.24cm D 2.0cm

77. Which instrument is used to measure accurately the diameter of a thin metal wire? A 30 cm ruler B measuring tape C metre rule D micrometer screw gauge

78. Water drips from a tap into a measuring cylinder. The table shows the volume of water in the cylinder every minute for four minutes.

time / minutes volume of water/ cm3 0 0

1.0 27 2.0 57 3.0 83 4.0 112

What is the average volume of water collected in the cylinder each minute? A 22 cm3 B 28 cm3 C 56 cm3 D 57 cm3



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79. Which pair of quantities includes one scalar and one vector? A mass time B temperature time C temperature velocity D velocity weight

80. Which row shows the best choice of measuring instruments to obtain accurate values for the distances shown?

diameter of wire height of bench length of laboratory A measuring tape measuring tape micrometer screw gauge B metre rule micrometer screw gauge measuring tape C micrometer screw gauge measuring tape metre rule D micrometer screw gauge metre rule measuring tape

81. A measuring cylinder contains some water. When a stone is put

in the water, the level rises. What is the volume of the stone? A 50 cm3 B 70 cm3 C 75 cm3 D 125 cm3

82. A metre rule is used to measure a length. Which reading is shown to the nearest millimetre? A 0.7 m B 0.76 m C 0.761 m D 0.7614 m

83. A student uses a stopwatch to time a runner running around a circular track. The runner runs two laps (twice around the track). The diagrams show the reading on the stopwatch when the runner starts running, at the end of the first lap, and at the end of the second lap.

What is the time taken for the runner to run the second lap? A 0 min 50s B 1 min 10s C 1min 13s D 2 min 03s



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84. The diagram shows an enlarged drawing of the end of a metre rule. It is being used to measure the length of a small feather.

What is the length of the feather? A 19mm B 29mm C 19cm D 29cm

85. A cylindrical can is rolled along the ruler shown in the diagram.

The can rolls over twice. What is the circumference (distance all round) of the can? A 13 cm B 14 cm C 26 cm D 28 cm

86. Which quantity is measured in newtons? A density B energy C pressure D weight

87. A student wishes to measure accurately the volume of approximately 40 cm3 of water. She has two measuring cylinders, a larger one that can hold 100cm3 , and a smaller one that can hold 50cm3 . The water forms a meniscus where it touches the glass.

Which cylinder should the student use and which water level should she use to ensure an accurate result? cylinder water level A larger one bottom of meniscus B larger one top of meniscus C smaller one bottom of meniscus D smaller one top of meniscus



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88. The diagrams show the readings on a measuring cylinder before and after a small metal cube is added.

How many more identical cubes can be added to the cylinder, without causing the water to overflow? Do not include the cube already in the cylinder. A 1 B 2 C 3 D 4

89. A stopwatch is used to time a runner in a race. The diagrams show the stopwatch at the start and at the end of the race. How long did the runner take to run the race? A 70.00 seconds B 110.00 seconds C 115.20 seconds D 155.20 seconds

90. What is the most accurate and precise method to measure the thickness of a coin? A Use a micrometer screw gauge. B Use a ruler and look at the scale perpendicularly. C Use a top pan balance. D Use the displacement method with water in a measuring cylinder.

91. A length of cotton is measured between two points on a ruler.

When the length of cotton is wound closely around a pen, it goes round six times.

What is the distance once round the pen? A 2.2 cm B 2.6 cm C 13.2 cm D 15.6 cm



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92. Diagram 1 shows a measuring cylinder containing water. A metal weight with a cork attached by a thread is held above the water. Diagram 2 shows the apparatus after the weight has been lowered into the water. Diagram 3 shows the apparatus after the weight and the cork have been submerged.

What is the volume of the cork? A 20 cm3 B 30 cm3 C 45 cm3 D 70 cm3

93. A ruler is used to measure the length of a nail.

What is the length of the nail? A 1.3cm B 2.9cm C 5.2cm D 8.1cm

94. A stopwatch is used to time an athlete running 100 m. The timekeeper forgets to reset the watch to zero before using it to time another athlete running 100m.

How long does the second athlete take to run 100m? A 11.2s B 11.4s C 12.4s D 23.8s



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95. A student measures the volume of a cork. He puts some water into a measuring cylinder and then one glass ball. He puts the cork and then a second, identical glass ball into the water as shown.

Diagram 1 shows the first water level. Diagram 2 shows the water level after one glass ball is added. Diagram 3 shows the water level after the cork and the second glass ball are added. What is the volume of the cork? A 30 cm3 B 40 cm3 C 50 cm3 D 100 cm3

96. A pendulum is set in motion and timed. The time measured for 20 complete swings is 30 s. What is the time for one complete swing of the pendulum? A 0.67 s B 0.75 s C 1.5 s D 3.0 s

97. The diagram shows part of a micrometer screw gauge.

What is the smallest reading that can be achieved using this micrometer screw gauge? A 0.0001 mm B 0.01 mm C 0.1 mm D 1 mm

98. The diagram shows a stopwatch, originally set at 00:00. When a car was first seen, the stop-start button was pressed. When the car passed the observer, the stopwatch showed 01:06. How long did the car take to reach the observer? A 1.06 seconds B 6 seconds C 66 seconds D 106 seconds



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99. A girl uses a rule to measure the length of a metal rod. Because the end of the rule is damaged, she places one end of the rod at the 1 cm mark as shown.

How long is the metal rod? A 43 mm B 46 mm C 53 mm D 56 mm

100. A floor is covered with square tiles. The diagram shows a ruler on the tiles.

How long is one tile? A 3 cm B 6 cm C 9 cm D 12 cm



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