Physical
Quantities
As Physics.
By Yasir Naseer.
0314-5162342
Learning outcomes
Candidates should be able to:
(a) show an understanding that all physical
quantities consist of a numerical
magnitude and a unit
(b) recall the following SI base quantities and their
units: mass (kg),
length (m), time (s), current (A), temperature (K),
amount of substance (mol)
(c) express derived units as products or quotients of
the SI base units and
use the named units listed in this syllabus as
appropriate
(d) use SI base units to check the homogeneity of
physical equations
(e) show an understanding of and use the
conventions for labelling graph
axes and table columns as set out in the ASE
publication Signs, Symbols and Systematics.
(f) use the following prefixes and their symbols to
indicate decimal submultiples or multiples of both
base and derived units: pico (p), nano (n),
micro (μ), milli (m), centi (c), deci (d), kilo (k), mega
(M), giga (G), tera (T)
(g) make reasonable estimates of physical quantities
included within the Syllabus.
For Quick Revision See next Page
Estimtions.
Past Paper Questions
Fundamental & Derived quantities
Q-1
Which definition is correct and uses only quantities rather than units?
A
Density is mass per cubic metre.B
Potential difference is energy per unit current.
C
Pressure is force per unit area. D
Speed is distance travelled per second.
Q-2
Which row shows a base quantity with its correct SI unit?
Q-3
Which of the following pairs of units are both SI base units?
A
C
ampere, degree Celsius
coulomb, degree Celsius
B
D
ampere, kelvin
coulomb, kelvin
Q-4
Which is a pair of SI base units?
Q-5
Which row shows an SI base quantity with its correct unit?
Q-6
What is the unit of weight in terms of SI base unit(s)?
Q-7
A
kg m s–1
B
kg m s–2
C
Which of the following could be measured in the same units as force?
energy / distance
N
D
J m –1
energy x distance
C
Q-8
energy / time
D
momentum x distance
The unit of work, the joule, may be defined as the work done when the point of application of a force of
1 newton is moved a distance of 1 metre in the direction of the force. Express the joule in terms of the
base units of mass, length and time, the kg, m and s.
A
C
kgm–1s2
kgm2 s–1
B
D
kgm2 s–2
kg s–2
Q-9
The SI unit for potential difference (the volt) is given, in base units, by
A
Q-10
kg m A–1s–3.
B
m2A–1s–2
C
kg m2s–2
D
kg m2A–1s–3.
C
m 2 kg s –3
D
N m s –1
What is the unit watt in terms of SI base units?
A
**Q-11
J s–1
B
m 2 kg s–1
Which unit is equivalent to the coulomb?
A
ampere per second
B
joule per volt
C
watt per ampere
D
watt per volt
(Winter 13)
Q-12
The unit of resistivity, expressed in terms of
base units, is given by
kg x 3 y –2 z –3 .
Which base units are x, y and z?
Q-13
For each of the four concepts listed in the left hand column, place a tick by the correct example of that
concept in the appropriate box.
Q-14
Classify each of the terms in the left-hand column by placing a tick in the relevant box.
Determination of S.I Units and Equations
Q-1
The product of pressure and volume has the same SI base units as
A
energy.
B force. C
area/force
D length / force .
Q-2
When a beam of light is incident on a surface, it delivers energy to the surface. The intensity of the beam is
defined as the energy delivered per unit area per unit time. What is the unit of intensity, expressed in SI base
units?
A
Q-3
kg m–2 s–1
B
kg m2 s–3
C
kg s–2
D
kg s–3
One property Q of a material is used to describe the behaviour of sound waves in the material. Q is defined as the
pressure P of the sound wave divided by the speed v of the wave and the surface area A of the material through
which the wave travels:
𝒑
Q=
.
𝒗𝑨
What are the SI base units of Q?
A
kg m- 2 s –3
B
kg m –3 s –1
C
kg –1m –4 s
D
kg m –2 s –2
Q-4
The table contains some quantities, together with their symbols and units.
Which expression has the units of energy?
The momentum of an object of mass m is p. Which quantity has the same base units as p2 /m ?
Q-5
( momentum is product of mass and velocity)
A
energy
B
force
C
power
D
velocity
Q-6
In the expressions below a is acceleration, F is force, m is mass, t is time, v is velocity. Which
expression represents energy?
Q-7
The equation relating pressure and density is p = ρgh .How can both sides of this equation be
written in terms of base units?
Q-8
A
[N m–1] = [kg m–3] [m s–1] [m]
B
[N m–2] = [kg m–3] [m s–2] [m]
C
[kg m–1 s–2] = [kg m–3] [m s–2] [m]
D
[kg m–1 s–1] = [kg m–1] [m s–2] [m]
The frictional force F on a sphere falling through a fluid is given by the formula
F = 6πaηv
where a is the radius of the sphere, η is a constant relating to the fluid and v is the velocity of the
sphere. What are the units of η ?
A
Q-9
kg m s–1
B
kg m–1s–1
C
kg m s–3
D
kg m3s–3
A metal sphere of radius r is dropped into a tank of water. As it sinks at speed v, it experiences a
drag force F given by F = kr v, where k is a constant. What are the SI base units of k?
A
kg m2s–1
B
kg m–2s–2
C
kg m–1s–1
D
kg m s–2
Q-10
The drag force F acting on a moving sphere obeys an equation of the form F = kAv2, where A represents
the sphere’s frontal area and v represents its speed. What are the base units of the
constant k ?
Q-11
A
kg m5s–4
B
kg m–2s–1
C
kg m–3
D
kg m–4 s2
Which formula could be correct for the speed v of ocean waves in terms of the density of seawater,
the acceleration of free fall g, the depth h of the ocean and the wavelength ?
]
Q-12
The spring constant k of a coiled wire spring is given by the equation
where r is the radius of the wire, n is the number of turns of wire and R is the radius of each of the
turns of wire. The quantity G depends on the material from which the wire is made. What is a suitable
for G?
(Winter-13)
unit
A
Q-13
N m–2
B
N m–1
C
Nm
D
N m2
At temperatures close to 0 K, the specific heat capacity c of a particular solid is given by
c = bT3,
where T is the thermodynamic temperature and b is a constant characteristic of the solid. What are
units of constant b, expressed in SI base units?
Q-14
A
m2s–2K–3
B
m2s–2K–4
C
kg m2s–2K–3
D
kg m2s–2K–4
A cylindrical tube rolling down a slope of inclination θ moves a distance L in time T. The equation
relating these quantities is
(Winter 11)+ winter 15
Where a is the internal radius of the tube and P and Q
are constants.Which line gives the correct units for P
and Q?
Q-15
The Reynolds number R is a constant used in the study of liquids flowing through pipes. R is a
pure number with no unit.
R = ρvD/μ
where ρ is the density of the liquid, v is the speed of the liquid and D is the diameter of the pipe
through which the liquid flows. What are the SI base units of μ?
A kg m s
B kg m–1s
C kg m s–1
D
kg m–1s–1
Q-16
The time T for a satellite to orbit the Earth is given by
where R is the distance of the satellite from the centre of the Earth, M is the mass of the Earth, and K is a constant.
(a) Determine the SI base units of K.
SI base units of K ............................... [2]
(b) A metal wire has original length l0. It is then
suspended and hangs vertically as shown in Fig.
The weight of the wire causes it to stretch. The elastic
potential energy stored in the wire
is E.
(i)
Show that the SI base units of E are kg m2 s–2.
the
Winter -13
(ii) The elastic potential energy E is given by
E = C 2 g 2 A l0 3
where is the density of the metal, g is the acceleration of free fall, A is the cross-sectional area of the wire
and C is a constant. Determine the SI base units of C.
SI base units of C .................................................. [3]
Q-17
(a)
The speed v of sound in a gas is given by the expression
,
where p is the pressure of the gas of density . is a constant. Given that p has the base units of
kgm1s-2, show that the constant has no unit.
[3]
(b)
The pressure p at a depth h in an incompressible fluid of density is given by
p = gh,
where g is the acceleration of free fall. Use base units to check the homogeneity of this equation.
[3]
Q-18 (a) (i) State the SI base units of volume.
Summer - 12
base units of volume ................................................. [1]
(ii) Show that the SI base units of pressure are
kg m –1 s –2.
(b) The volume V of liquid that flows through a pipe in time t is given by the equation
where P is the pressure difference between the ends of the pipe of radius r and length l. The constant C
depends on the frictional effects of the liquid. Determine the base units of C.
base units of C .............................................. [3]
Q-19
(a) Determine the SI base units of power.
SI base units of power ......................................... [3]
(b) Fig. 19.1 shows a turbine that is used to generate electrical power from the wind.
The power P available from the wind is given by
P = CL 2 v 3
where L is the length of each blade of the turbine,
is the density of air,
v is the wind speed,
C is a constant.
(i)
Show that C has no units.
[1]
Determination of unknown Powers
Q-1
The maximum theoretical power P of a wind turbine is given by the equation
P = kρAv n
where ρ is the density of air, A is the area swept by the turbine blades, v is the speed of the air
and k is a constant with no units. What is the value of n ?
A
Q-2
1
B
2
C
3
D
4
The drag coefficient Cd is a number with no units. It is used to compare the drag on different cars
at different speeds. It is given by the equation
where F is the drag force on the car, ρ is the density of the air, A is the cross-sectional area of the
car and v is the speed of the car. What is the value of n?
A1
Q-3
B
2
C
3
D
4 (Winter 13)
The speed v of a liquid leaving a tube depends on the change in pressure ΔP and the density ρ of
the liquid. The speed is given by the equation
where k is a constant that has no units. What is the value of n ?
*Q-4
(a) The current in a wire is I. Charge Q passes one point in the wire in time t. State
(i) the relation between I, Q and t,
....................................................................................................................................
[1]
(ii) which of the quantities I, Q and t are base quantities.
.........................................................................................................................................
(b)
[2]
The current in the wire is due to electrons, each with charge q, that move with speed v along the wire.
There are n of these electrons per unit volume. For a wire having a cross-sectional area S, the current I
is given by the equation
I=
nSqvk,
where k is a constant.
(i) State the units of I, n, S, q and v in terms of the base units.
I
.............................................................................................................................
n
.............................................................................................................................
S
.............................................................................................................................
q
.............................................................................................................................
v
.............................................................................................................................
(ii) By considering the homogeneity of the equation, determine the value of k.
[3]
Q-5
(a) Two of the SI base quantities are mass and time. State three other SI base quantities.
1. .....................................................................................................................................
2. .....................................................................................................................................
3. .....................................................................................................................................
(b)
[3]
A sphere of radius r is moving at speed v through air of density . The resistive force F
acting on the sphere is given by the expression
F = Br2vk
where B and k are constants without units.
(i) State the SI base units of F, and v.
F


..............................................................................................................................
..............................................................................................................................
V
..............................................................................................................................
[3]
(ii) Use base units to determine the value of k.
k = ................................................ [2]
B
Prefixes
Q-`1
Q-2
The notation μs is used as an abbreviation for a certain unit of time. What is the name and value of
this unit?
Decimal sub-multiples and multiples of units are indicated using a prefix to the unit. For example,
the prefix milli (m) represents 10–3. Which of the following gives the sub-multiples or multiples represented by
pico (p) and giga (G)?
+
Q-3
Which line in the table correctly indicates the prefixes micro, nano and pico?
Q- 4
Which list shows increasing lengths from beginning to end?
A
1 cm 1 nm 1 mm 1 μm
C
1 nm
1 μm
1 mm
1 cm
B
1 μm
1 mm 1 nm 1 cm
D
1 mm 1 cm
1 μm
1 nm
Q-5
Q-6
Which statement, involving multiples and sub-multiples of the base unit metre (m), is correct?
Q-10
1 mm = 106 μm
D
1 km = 106
C
10–12
D
C
10 0
𝟏𝒖𝒎
𝟏 𝑮𝒎
10–3
mm
?
B
10–9
B
10
10–15
10 –9
–6
D
10
pico x mega
micro x giga
B
3
nano x kilo
D
milli x tera
A
5 kJ → 5 mJ → 5 MJ → 5 nJ
B
5 nJ → 5 kJ → 5 MJ → 5 mJ
C
5 nJ → 5 mJ → 5 kJ → 5 MJ
D
5 mJ → 5 nJ → 5 kJ → 5 MJ
A student measures a current as 0.5 A. Which of the following correctly expresses this result?
50 mA
B
What is equivalent to 2000 microvolts?
A
Q- 12
C
Five energies are listed. Starting with the smallest first, what is the order of increasing magnitude of these
energies?
A
Q-11
1 nm = 10–6 m
Which product-pair of metric prefixes has the greatest magnitude?
A
C
Q-9
B
What is the ratio
A
Q-8
1 pm = 10–9 m
What is the ratio
A
Q-7
A
2 μJ C–1 B
2
mV
50 MA
C
500 mA
D
500MA
Summer 15
C
2 pV
D
2000 mV
Complete Fig. 12.1 to show each prefix with its symbol and power-of-ten. prefix symbol power-of-ten
[4]
Estimations
Q-1
Which row gives reasonable estimates for the mass and the speed of an adult running?
Summer 15
Q-2
What is the approximate kinetic energy of an Olympic athlete when running at maximum speed
during a 100 m race?
(winter 12)
A
Q-3
400 J
40 000 J
D
400 000 J
The kinetic energy of a bus travelling on an expressway is 30 000 J.
The power of a domestic light is 300 W.
The temperature of a hot oven is 300 K.
The volume of air in a car tyre is 0.03 m 3.
Which estimate is realistic?
A
B
C
D
Q-5
4000 J C
Which estimate is realistic?
A
B
C
D
Q-4
B
The kinetic energy of a bus travelling on an expressway is 30 000 J.
The power of a domestic light is 300 W.
The temperature of a hot oven is 300 K.
The volume of air in a car tyre is 0.03 m3.
(WINTER 13)
A 1.5 V cell supplies 0.20 A to a lamp for seven hours before the lamp goes out.
What is a sensible estimate for the initial chemical energy content of the cell?
A 1 × 102 J
B
1 × 104 J
C 1 × 106J
D
(WINTER 12)
1 × 10 8 J
Q-6
In making reasonable estimates of physical quantities, which statement is not correct?
A
B
C
D
Q-7
Q-8
The frequency of sound can be of the order of GHz.
The wavelength of light can be of the order of 600 nm.
The Young modulus of a metal can be of the order of 1011 Pa.
Beta particles are associated with one unit of negative charge.
Which statement is incorrect by a factor of 100 or more?
A
Atmospheric pressure is about 1 × 105 Pa.
B
Light takes 5 × 102 s to reach us from the Sun.
C
The frequency of ultra-violet light is 3 × 1012 Hz.
D
The life-span of a man is about 2 × 109 s.
For which quantity is the magnitude a reasonable estimate?
A
frequency of a radio wave 500 pHz
B
C
D
(Summer 13)
Summer 12
mass of an atom 500 μg
the Young modulus of a metal 500 kPa
wavelength of green light 500 nm
Q-9 Make reasonable estimates of the following quantities.
Summer - 08
(a) the frequency of an audible sound wave
frequency = ........................................... Hz [1]
(b) the wavelength, in nm, of ultraviolet radiation
wavelength = ........................................ nm [1]
(c) the mass of a plastic 30 cm ruler
mass = .............................................. g
[1]
(d) the density of air at atmospheric pressure
density = ..................................... kg m–3 [1]
Q-10 Make estimates of the following quantities.
(a) the thickness of a sheet of paper
thickness = ....................................... mm
[1]
time = ........................................... s
[1]
weight = .......................................... N
[1]
(b) the time for sound to travel 100 m in air
(c) the weight of 1000 cm3 of water
Q-11 Make reasonable estimates of the following quantities.
(a) mass of an apple
Summer- 05
mass = ............................................... kg
[1]
number = ...................................................
[1]
wavelength = .......................................... m
[1]
(b) number of joules of energy in 1 kilowatt-hour
(c) wavelength of red light in a vacuum
(d) pressure due to a depth of 10 m of water
pressure = .............................................. Pa [1]
Graphical Analysis
Q-1
A light-meter measures the intensity I of the light falling on it. Theory suggests that I varies inversely as the
square of the distance d.
Summer -12
Which graph of the results supports this theory?
Q-1 (a) State the SI base units of force.
......................................................................................................................................
Summer-13
[1]
(b) Two wires each of length l are placed parallel to each other a distance x apart, as shown in Fig.1.
Fig. 1
Each wire carries a current I. The currents give rise to a force F on each wire given by
where K is a constant.
(i) Determine the SI base units of K.
units of K ................................................. [2]
(ii) On Fig. 2, sketch the variation with x of F. The quantities I and l remain constant.
[2]
(iii) The current I in both of the wires is varied.
On Fig. 1.3, sketch the variation with I of F. The quantities x and l remain constant.
Fig.3
Test Your-Self
[1]
Q-1. With the aid of an example, explain the statement “The magnitude of a physical quantity is written as the
product of a number and a unit”.
................................................................................................................................................................................
................................................................................................................................................................................
........................................................................................................................................................
(2)
Explain why an equation must be homogeneous with respect to the units if it is to be correct.
...........................................................................................................................................................................
..................................................................................................................................................................
Write down an equation which is homogeneous, but still incorrect.
(1)
............................................................................................................................................
............................................................................................................................................
(2)
Q-2. State what is meant by “an equation is homogeneous with respect to its units”.
............................................................................................................................................
............................................................................................................................................
(1)
Show that the equation
is homogeneous with respect to its units.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
(3)
Explain why an equation may be homogeneous with respect to its units but still be incorrect.
............................................................................................................................................
............................................................................................................................................
(1)
(Total 5 marks)
Q-3. The joule is the SI unit of energy. Express the joule in the base units of the SI system.
..................................................................................................................................
..................................................................................................................................
(1)
A candidate in a physics examination has worked out a formula for the kinetic energy E of a solid sphere spinning
about its axis. His formula is
E=
1
2
r 5f 2
where ρ is the density of the sphere, r is its radius and f is the rotation frequency. Show that this formula is
homogeneous with respect to base units.
(3)
Why might the formula still be incorrect?
..................................................................................................................................
..................................................................................................................................
(1)
(Total 5 marks)
Q-4 (a) Show that the SІ base units of power are kg m 2 s–3.
Summer 14 / 22
[3]
(b)
The rate of flow of thermal energy Q/ t in a material is given by/
Q / t = CAT/x
where A is the cross-sectional area of the material,
T
is the temperature difference across the thickness of the material,
X
is the thickness of the material,
C
is a constant.
Determine the SІ base units of C.
base units .......................................................... [4]
Q-5 (a) Use the definition of power to show that the SI base units of power are kg m2 s–3. Summer 15 / 21
[2]
(b) Use an expression for electrical power to determine the SI base units of potential difference.
units ...........................................................[2]
Q-6 (a) The distance between the Sun and the Earth is 1.5 × 1011 m. State this distance in Gm.
distance = ................................................... Gm [1]
(b) The distance from the centre of the Earth to a satellite above the equator is 42.3 Mm. The
radius of the Earth is 6380 km. A microwave signal is sent from a point on the Earth directly below the satellite.
Calculate the time taken for the microwave signal to travel to the satellite and back.
time = ....................................................... s [2]
(c) The speed v of a sound wave through a gas of density and pressure P is given by
Summer 15 / 23
where C is a constant. Show that C has no unit.
[3]
Answers.
Fundamental & Derived quantities
Q-1
C
Q-2
A
Q-3
B
Q-4
B
Q-5
B
Q-6
B
Q-7
A
Q-8
B
Q-9
D
Q-10
C
Q-11
B
Q-12 B
Q-13
Q-14
Length,Ampere,K.E, Weight
Determination of S.I Units and Equations
Q-1
A
Q-2
D
Q-3
A
Q-4
A
Q-5
A
Q-6
B
Q-7
C
Q-8
B
Q-9
C
Q-10
C
Q-11
A
Q-12 A
Q-13
B
Q-14
B
Q-15 D
Q-16
a) kg s 2m
b) ii- ms2kg
-1
Q-17
Homogeneous
Q-18
kg m-1s
Q-19
-3
-1
Units of power = kg m2s-2
Determination of unknown Powers
Q-1
C
Q-2
B
Q-4
K = 1
Q-5
K = 2
Q-3
A
Prefixes
Q-1
A
Q-2
C
Q-3
C
Q-4
C
Q-5
D
Q-6
D
Q-7
D
Q-8
D
Q-10
C
Q-11
B
Q-12
10
-9
,
C
,
Mega
,
Q-9
C
Tera
Estimations
Q-1
C
Q-2
B
Q-3
D
Q-4
D
Q-5
B
Q-6
B
Q-8
D
Q-7* C\D
Q-9
Q-10
.25 mm
, 0.33 seconds
,
10
N
Q-11
Graphical Analysis
Q-1
D
Q-2