Physical Quantities and Measurement Techniques

Chapter 1 MCQs

1

A student measures the length of a metal rod using a ruler. The left end of the rod is at the 2.4 cm mark and the right end is at the 18.9 cm mark.

What is the length of the rod?

A 16.3 cm
B 16.5 cm
C 18.9 cm
D 21.3 cm

2

A ruler has a damaged zero mark. A student uses the 1.0 cm mark as the starting point to measure a pencil. The other end of the pencil is at 14.8 cm.

What is the length of the pencil?

A 13.8 cm
B 14.8 cm
C 15.8 cm
D 148 mm

3

A student measures the thickness of 100 sheets of paper and obtains a value of 8.0 mm.

What is the average thickness of one sheet?

A 0.008 mm
B 0.080 mm
C 0.80 mm
D 8.0 mm

4

A student wants to measure the diameter of a thin wire as accurately as possible.

Which instrument is most suitable?

A measuring tape
B metre rule
C micrometer screw gauge
D measuring cylinder

5

A student wants to measure the internal diameter of a test tube.

Which instrument is most suitable?

A measuring cylinder
B micrometer screw gauge
C ruler only
D vernier calipers

6

A micrometer screw gauge has a main scale reading of 5.5 mm. The circular scale reading is 34 divisions. Each division is 0.01 mm.

What is the micrometer reading?

A 5.34 mm
B 5.50 mm
C 5.84 mm
D 8.90 mm

7

A micrometer screw gauge shows:

main scale reading = 3.0 mm
circular scale reading = 47 divisions
each circular scale division = 0.01 mm

What is the reading?

A 3.047 mm
B 3.47 mm
C 4.70 mm
D 7.70 mm

8

A micrometer has a zero error of +0.04 mm. The observed reading for a wire is 2.63 mm.

What is the correct diameter of the wire?

A 2.59 mm
B 2.63 mm
C 2.67 mm
D 4.63 mm

9

A micrometer has a zero error of −0.02 mm. The observed reading for a ball bearing is 6.38 mm.

What is the correct diameter?

A 6.36 mm
B 6.38 mm
C 6.40 mm
D 6.58 mm

10

A student winds 40 turns of a thin wire tightly around a pencil. The total width of the turns is 12.0 mm.

What is the diameter of the wire?

A 0.030 mm
B 0.30 mm
C 3.0 mm
D 480 mm

Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

11

A student measures the diameter of a wire by winding 25 turns around a pencil. The total width is 7.5 mm.

What is the diameter of the wire?

A 0.03 mm
B 0.30 mm
C 3.0 mm
D 187.5 mm

12

A measuring cylinder contains 45 cm³ of water. An irregular stone is fully submerged and the water level rises to 72 cm³.

What is the volume of the stone?

A 27 cm³
B 45 cm³
C 72 cm³
D 117 cm³

13

A student places an irregular solid into a measuring cylinder containing water. The level rises from 38 cm³ to 61 cm³.

The mass of the solid is 92 g.

What is the density of the solid?

A 0.25 g/cm³
B 1.5 g/cm³
C 4.0 g/cm³
D 23 g/cm³

14

A liquid has a volume of 80 cm³. Its mass is 64 g.

What is the density of the liquid?

A 0.80 g/cm³
B 1.25 g/cm³
C 16 g/cm³
D 5120 g/cm³

15

A metal cube has sides of length 2.0 cm. Its mass is 64 g.

What is the density of the metal?

A 4.0 g/cm³
B 8.0 g/cm³
C 16 g/cm³
D 32 g/cm³

16

A rectangular block has dimensions 4.0 cm × 3.0 cm × 2.0 cm. Its mass is 180 g.

What is its density?

A 7.5 g/cm³
B 15 g/cm³
C 24 g/cm³
D 2160 g/cm³

17

A student wants to measure the volume of a small irregular stone that sinks in water.

Which apparatus is needed?

A balance and stopwatch
B measuring cylinder and water
C ruler and stopwatch
D thermometer and measuring tape

18

A student wants to find the density of an irregular stone that sinks in water.

Which apparatus is needed?

A balance, measuring cylinder and water
B balance and thermometer only
C ruler and measuring tape only
D stopwatch and measuring cylinder only

19

A small piece of cork floats in water. A student wants to find its volume using a measuring cylinder.

Which method is best?

A Put the cork on the water and measure the rise in water level.
B Push the cork fully underwater using a thin pin and measure the rise in water level.
C Measure the mass of the cork and divide by water density.
D Measure only the part of the cork below the water surface.

20

A student wants to measure the volume of a regular wooden cube.

Which method gives the volume directly from length measurements?

A length × width
B length × width × height
C mass ÷ density of water
D final cylinder reading − initial cylinder reading

21

A student times 20 oscillations of a pendulum. The total time is 31.0 s.

What is the period of the pendulum?

A 0.645 s
B 1.55 s
C 20.0 s
D 620 s

22

A pendulum makes 30 complete oscillations in 48.0 s.

What is its period?

A 0.625 s
B 1.60 s
C 18.0 s
D 1440 s

23

A student wants to measure the period of a pendulum accurately.

Which method is best?

A Measure one oscillation once.
B Measure half an oscillation and double it.
C Measure 20 oscillations and divide the time by 20.
D Measure the length of the string and divide by 20.

24

A stopwatch has a reaction-time uncertainty of about 0.2 s. A student measures one oscillation of a pendulum as 1.5 s.

Why is it better to time 20 oscillations?

A It makes the pendulum move faster.
B It increases the total measured time, reducing percentage uncertainty.
C It reduces the actual period of the pendulum.
D It removes air resistance completely.

25

Which quantity is a scalar?

A acceleration
B displacement
C force
D speed

Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

26

Which list contains only scalar quantities?

A distance, mass, energy
B displacement, mass, velocity
C force, speed, time
D weight, acceleration, temperature

27

Which list contains only vector quantities?

A acceleration, displacement, force
B distance, energy, temperature
C mass, momentum, speed
D time, speed, volume

28

Which row correctly classifies the quantities?

	scalar	vector
A	velocity	speed
B	force	mass
C	distance	displacement
D	weight	energy

29

A student walks 3 m east and then 4 m north.

What is the magnitude of her resultant displacement?

A 1 m
B 5 m
C 7 m
D 12 m

30

Two perpendicular forces act on an object.

8 N horizontally
15 N vertically

What is the magnitude of the resultant force?

A 7 N
B 17 N
C 23 N
D 120 N

31

Two perpendicular forces of 5 N and 12 N act on a body.

What is the resultant force?

A 7 N
B 13 N
C 17 N
D 60 N

32

Two perpendicular displacements are 9.0 m and 12.0 m.

What is the resultant displacement?

A 3.0 m
B 15.0 m
C 21.0 m
D 108 m

33

A force of 6 N acts east and a force of 8 N acts north.

Which statement is correct?

A The resultant is 2 N.
B The resultant is 10 N.
C The resultant is 14 N.
D The resultant is 48 N.

34

A student adds two vector quantities by simple addition of their magnitudes.

When is this method definitely correct?

A when the vectors are at right angles
B when the vectors act in opposite directions
C when the vectors act in the same direction
D when the vectors have different units

35

Which pair of quantities cannot be added together to give a meaningful physical result?

A distance and distance
B force and force
C mass and time
D displacement and displacement

36

A student records a length as 12.347 cm using a metre rule marked in millimetres.

Why is this unsuitable?

A A metre rule cannot measure lengths in centimetres.
B A metre rule cannot measure to 0.001 cm precision.
C A metre rule cannot measure objects longer than 10 cm.
D Length must always be recorded in metres.

37

A student measures a length using a ruler marked in millimetres.

Which reading is most appropriate?

A 4 cm
B 4.3 cm
C 4.327 cm
D 4.3279 cm

38

A student measures the mass of an object.

Which instrument is most suitable?

A ammeter
B electronic balance
C force meter
D measuring cylinder

39

A student measures the weight of an object.

Which instrument is most suitable?

A electronic balance
B force meter
C measuring cylinder
D stopwatch

40

A student measures the volume of a liquid.

Which instrument should be used?

A balance
B force meter
C measuring cylinder
D micrometer screw gauge

Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

41

A student wants to measure the volume of a drop of water accurately.

Which method is best?

A Measure the volume of one drop directly using a measuring cylinder.
B Count 100 drops into a measuring cylinder and divide the volume by 100.
C Measure the mass of one drop using a ruler.
D Use a stopwatch to time the drop falling.

42

A student wants to determine the average diameter of a small spherical bead.

Which method is best?

A Measure the bead once using a metre rule.
B Measure several beads in a row and divide by the number of beads.
C Put the bead in a stopwatch and record the time.
D Measure the mass of the bead using a measuring cylinder.

43

A student measures the time for 10 swings of a pendulum three times.

The readings are:

15.8 s
16.0 s
16.2 s

What is the average period of the pendulum?

A 1.58 s
B 1.60 s
C 16.0 s
D 48.0 s

44

A car travels 120 m north.

Which statement about the quantity 120 m north is correct?

A It is a scalar distance.
B It is a vector displacement.
C It is a scalar speed.
D It is a vector mass.

45

Which quantity has magnitude but no direction?

A acceleration
B force
C temperature
D velocity

46

A student says, “The resultant of two perpendicular forces is found by adding their magnitudes.”

Why is this incorrect?

A Perpendicular forces must be subtracted.
B Perpendicular forces must be multiplied.
C Perpendicular forces must be combined using Pythagoras.
D Perpendicular forces have no resultant.

47

Two forces act at right angles. Their resultant is 25 N. One force is 7 N.

What is the magnitude of the other force?

A 18 N
B 24 N
C 32 N
D 168 N

48

Two perpendicular vectors have magnitudes 10 units and 24 units.

What is the magnitude of the resultant?

A 14 units
B 26 units
C 34 units
D 240 units

49

A student walks 6 m east and 8 m west.

What is the magnitude of the resultant displacement?

A 2 m
B 10 m
C 14 m
D 48 m

50

A student walks 6 m east and 8 m north.

What is the magnitude of the resultant displacement?

A 2 m
B 10 m
C 14 m
D 48 m

Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

Answer Key

Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	B	11	B	21	B	31	B	41	B
2	A	12	A	22	B	32	B	42	B
3	B	13	C	23	C	33	B	43	B
4	C	14	A	24	B	34	C	44	B
5	D	15	B	25	D	35	C	45	C
6	C	16	A	26	A	36	B	46	C
7	B	17	B	27	A	37	B	47	B
8	A	18	A	28	C	38	B	48	B
9	C	19	B	29	B	39	B	49	A
10	B	20	B	30	B	40	C	50	B

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

Detailed Explanations

1. B

Length = final ruler reading − initial ruler reading
Length = 18.9 − 2.4 = 16.5 cm
C is wrong because 18.9 cm is only the final mark, not the length.
D is wrong because you do not add the two readings.

2. A

Length = 14.8 − 1.0 = 13.8 cm
When the zero mark is damaged, start from another mark and subtract.
B is the final reading only.
C adds the readings, which is nonsense here.
D is 14.8 cm converted to mm, but the actual length is not 14.8 cm.

3. B

Thickness of 100 sheets = 8.0 mm
Thickness of 1 sheet = 8.0 / 100 = 0.080 mm
A is too small by a factor of 10.
C is too large by a factor of 10.
This is a classic “measure many and divide” question.

4. C

A thin wire needs a very precise instrument.
A micrometer screw gauge is used for small diameters and thicknesses.
A metre rule is not precise enough.
A measuring cylinder measures volume, not diameter.

5. D

The internal diameter of a test tube is best measured with vernier calipers.
Micrometer screw gauge is better for very small external diameters, like wire.
A ruler alone is too crude.
Measuring cylinder measures volume.

6. C

Main scale = 5.5 mm
Circular scale = 34 × 0.01 = 0.34 mm
Total reading = 5.5 + 0.34 = 5.84 mm
A ignores the 0.5 mm on the main scale.
B ignores the circular scale.

7. B

Main scale = 3.0 mm
Circular scale = 47 × 0.01 = 0.47 mm
Total reading = 3.0 + 0.47 = 3.47 mm
A has the wrong decimal place.
C treats 47 divisions as 4.7 mm, which is wrong.

8. A

Zero error = +0.04 mm
Positive zero error means the micrometer reads too high.
Correct reading = observed reading − zero error
Correct reading = 2.63 − 0.04 = 2.59 mm
C wrongly adds the error.

9. C

Zero error = −0.02 mm
Negative zero error means the micrometer reads too low.
Correct reading = observed reading + 0.02
Correct reading = 6.38 + 0.02 = 6.40 mm
A subtracts when it should add.

10. B

Diameter of one wire = total width / number of turns
Diameter = 12.0 / 40 = 0.30 mm
C is too large.
A is too small.
The whole point is to make the tiny diameter measurable by using many turns.

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

11. B

Diameter = total width / number of turns
Diameter = 7.5 / 25 = 0.30 mm
D is the result of multiplying instead of dividing.
C is 10 times too large.

12. A

Volume of stone = final volume − initial volume
Volume = 72 − 45 = 27 cm³
B is the original water volume only.
C is the final cylinder reading, not the stone’s volume.
D adds the values, which is the trap.

13. C

Volume of solid = 61 − 38 = 23 cm³
Density = mass / volume
Density = 92 / 23 = 4.0 g/cm³
A and B come from wrong division.
D uses volume as density.

14. A

Density = mass / volume
Density = 64 / 80 = 0.80 g/cm³
B is the inverse: 80 / 64.
C and D are calculation traps.

15. B

Volume of cube = side³
Volume = 2.0 × 2.0 × 2.0 = 8.0 cm³
Density = 64 / 8 = 8.0 g/cm³
A comes from using area instead of volume.
C and D are overcalculated traps.

16. A

Volume = 4.0 × 3.0 × 2.0 = 24 cm³
Density = 180 / 24 = 7.5 g/cm³
B is too high.
C is just the volume.
D is mass × volume, not density.

17. B

For an irregular stone that sinks, volume is measured by displacement of water.
Apparatus needed: measuring cylinder and water.
Balance is not needed if only volume is required.
Stopwatch and thermometer are irrelevant.

18. A

Density = mass / volume.
Mass is measured using a balance.
Volume of irregular stone is measured using measuring cylinder + water.
Therefore: balance, measuring cylinder and water.

19. B

Cork floats, so if it is just placed on water, only the submerged part displaces water.
To find full volume, push it fully underwater using a thin pin.
Then volume = rise in water level.
A and D only measure submerged volume, not total volume.

20. B

For a regular cuboid/cube:
Volume = length × width × height
A gives area, not volume.
D is for irregular objects using displacement.

21. B

Period = time for one oscillation
Period = total time / number of oscillations
Period = 31.0 / 20 = 1.55 s
C is the number of oscillations.
D multiplies instead of dividing.

22. B

Period = 48.0 / 30
Period = 1.60 s
A is the inverse.
C and D are not periods.

23. C

Best method: time many oscillations and divide.
This reduces percentage uncertainty caused by reaction time.
Measuring one oscillation gives a larger percentage error.
Measuring half an oscillation is even worse.

24. B

Reaction time uncertainty stays about the same.
Timing 20 oscillations gives a larger total time.
Percentage uncertainty = uncertainty / measured value × 100
Larger measured time means smaller percentage uncertainty.

25. D

Speed is a scalar because it has magnitude only.
Acceleration, displacement and force are vectors because they have magnitude and direction.
Big trap: speed is scalar, velocity is vector.

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

26. A

Distance, mass and energy are all scalars.
B is wrong because displacement and velocity are vectors.
C is wrong because force is a vector.
D is wrong because weight and acceleration are vectors.

27. A

Acceleration, displacement and force are all vectors.
B contains only scalars.
C is wrong because mass and speed are scalars.
D contains only scalars.

28. C

Distance is scalar.
Displacement is vector.
A is reversed because velocity is vector and speed is scalar.
B is reversed because force is vector and mass is scalar.
D is reversed because weight is vector and energy is scalar.

29. B

The two displacements are perpendicular:
- 3 m east
- 4 m north
Resultant² = 3² + 4² = 9 + 16 = 25
Resultant = 5 m
C is wrong because 3 + 4 only works in a straight line.

30. B

The forces are perpendicular.
Resultant² = 8² + 15²
Resultant² = 64 + 225 = 289
Resultant = 17 N
8–15–17 is a standard right-angle triangle.

31. B

Resultant² = 5² + 12²
Resultant² = 25 + 144 = 169
Resultant = 13 N
5–12–13 is one of Cambridge’s favourite little traps.

32. B

Resultant² = 9² + 12²
Resultant² = 81 + 144 = 225
Resultant = 15.0 m
Adding gives 21 m, but that would only be correct if both displacements were in the same direction.

33. B

6 N east and 8 N north are perpendicular.
Resultant² = 6² + 8² = 36 + 64 = 100
Resultant = 10 N
C is the straight-line addition trap.
D is multiplication, not resultant.

34. C

You can add vector magnitudes directly only when they act in the same direction.
If they act in opposite directions, subtract.
If they act at right angles, use Pythagoras.
If units are different, they cannot be added meaningfully.

35. C

Mass and time are different physical quantities.
They cannot be added to give a meaningful result.
Distance + distance can be meaningful.
Force + force can be meaningful.
Displacement + displacement can be meaningful if directions are considered.

36. B

A metre rule marked in millimetres can reasonably measure to about 0.1 cm.
12.347 cm means precision to 0.001 cm.
That is fake precision.
A metre rule can measure in cm, so A is wrong.
Length does not always need to be recorded in metres.

37. B

A ruler marked in millimetres can measure to the nearest mm.
1 mm = 0.1 cm
So 4.3 cm is sensible.
4 cm is too vague.
4.327 cm and 4.3279 cm are too precise for a normal ruler.

38. B

Mass is measured using an electronic balance.
Force meter measures weight/force.
Measuring cylinder measures volume.
Ammeter measures current.

39. B

Weight is a force.
Force is measured using a force meter.
Electronic balance measures mass, not weight.
Measuring cylinder measures volume.

40. C

Volume of a liquid is measured using a measuring cylinder.
Balance measures mass.
Force meter measures force.
Micrometer measures tiny lengths or diameters.

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

41. B

One drop has a very small volume, difficult to measure directly.
Count 100 drops into a measuring cylinder.
Volume of one drop = total volume / 100
This reduces percentage uncertainty.

42. B

A small bead is difficult to measure accurately once.
Place several beads in a row and measure the total length.
Average diameter = total length / number of beads.
Same logic as measuring wire turns or paper thickness.

43. B

Average time for 10 swings:
Average = (15.8 + 16.0 + 16.2) / 3 = 48.0 / 3 = 16.0 s
Period = 16.0 / 10 = 1.60 s
C is the average time for 10 swings, not one swing.

44. B

“120 m north” includes magnitude and direction.
Therefore it is a vector.
Since it describes change in position, it is displacement.
Distance would be just “120 m” without direction.

45. C

Temperature has magnitude only.
It has no direction.
So temperature is scalar.
Acceleration, force and velocity are vectors.

46. C

Perpendicular forces cannot be added directly.
Their resultant is found using Pythagoras:
R² = F₁² + F₂²
The dumb trap is adding them like they’re standing in a queue. They’re not. They’re at right angles.

47. B

Resultant = 25 N
One force = 7 N
Other force² = 25² − 7²
Other force² = 625 − 49 = 576
Other force = 24 N
This is the 7–24–25 triangle.

48. B

Resultant² = 10² + 24²
Resultant² = 100 + 576 = 676
Resultant = 26 units
10–24–26 is a right-angle triangle.
C is direct addition, which is wrong for perpendicular vectors.

49. A

6 m east and 8 m west are opposite directions.
Resultant displacement = 8 − 6 = 2 m
Direction would be west, but the question asks only for magnitude.
C would be total distance, not resultant displacement.

50. B

6 m east and 8 m north are perpendicular.
Resultant² = 6² + 8²
Resultant² = 36 + 64 = 100
Resultant = 10 m
This contrasts with Q49:
- opposite directions: subtract
- perpendicular directions: Pythagoras

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

High-Level Traps Tested

Trap	Correct Rule
Object does not start at zero	final reading − initial reading
Damaged ruler zero	start from another mark and subtract
Very small thickness/diameter	measure many together and divide
Micrometer reading	main scale + circular scale
Positive zero error	subtract it
Negative zero error	add its magnitude
Measuring mass	use balance
Measuring weight	use force meter
Measuring volume of liquid	use measuring cylinder
Irregular object volume	displacement method
Floating object volume	fully submerge it
Period of pendulum	total time / number of oscillations
Scalar	magnitude only
Vector	magnitude and direction
Same direction vectors	add
Opposite direction vectors	subtract
Perpendicular vectors	use Pythagoras
Regular solid volume	length × width × height
Density	mass / volume
Fake precision	do not record more decimal places than instrument allows

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