WorksheetsMeasurements A-level MCQs
Total questions: 55
Worksheet time: 2hrs 33mins
Which one of the following pairs comprises two SI base units?
ampere, degree celsius
ampere, kelvin
coulomb, degree celsius
coulomb, kelvin
Which one of the following lists contains only SI base units?
kelvin, metre, mole, ampere, kilogram
kilogram, metre, second, ohm, mole
kilogram, newton, metre, ampere, ohm
newton, kelvin, second, volt, mole
Which pair does not contain any SI base units?
ampere, mole
coulomb, metre
newton, ohm
second, volt
In terms of the base units of mass, length and time, the kg, m and s, what are the base units of work, the joule (J)?
kg m⁻¹ s²
kg m² s⁻²
kg m² s⁻¹
kg s⁻²
When a steel sphere of radius r falls at speed v through a liquid, it experiences a drag force F given by F = arv, where a is a constant. Which one of the following is a suitable SI unit for a?
N
N s⁻¹
N m² s⁻¹
N m⁻² s
What could be a correct expression for the speed of ocean waves in terms of its wavelength λ, the depth h of the ocean, the density ρ of sea-water, and the acceleration of free fall g?
gλ
hg
ρgh
ρg
The relationship between four physical quantities is given by the equation P = Q – RS. Given that the equation is homogeneous, which of the following statements must be correct?
P, Q, R and S all have the same units.
P, Q, R and S are all scalar quantities.
The product RS has the same units as P and Q.
The product RS is numerically equal to (Q – P).
Which one of the following expressions has different units from the other three?
density × volume × velocity
rate of change of momentum
the Young modulus × area
weight
What are the SI base units of pressure?
kg m s⁻¹
kg m⁻¹ s⁻²
kg m² s⁻²
kg m⁻² s⁻¹
What are the SI base units of specific heat capacity?
m s⁻² K⁻¹
m s⁻¹ K⁻¹
m² s⁻² K⁻¹
m² s⁻¹ K⁻¹
The energy E of a photon of electromagnetic radiation of frequency f is given by the expression E = hf. What are the SI base units of the Planck constant h?
kg m s-1
kg m2 s-1
kg m2 s-2
kg m2 s-3
In terms of kilogram (kg), metre (m), second (s) and ampere (A), what are the base units of potential difference (the volt)?
m and A only
s and A only
m, s and A only
kg, m, s and A
If an object of mass m has momentum p, which of the following quantities has identical base units to the expression mp2 ?
energy
force
power
velocity
Which one of the following expressions has a base unit that is not the second (s)?
1/frequency
capacitance × resistance
length+acceleration
mass ÷ spring constant
Which quantity has a unit with an alternative form in terms of just two different SI base units?
area
charge
current
force
What is a possible unit for electric field strength?
C m-1
N C-1
N m-1
N V-1
The ohm (Ω), the unit of resistance, has an alternative form V A-1. Which pair has a correct alternative form of the associated unit?
coulomb (C) & A s-1
farad (F) & V C-1
pascal (Pa) & N m-2
volt (V) & J C
Which pair consists of units that are not equivalent?
Wb m-2 ; T
J s-1 ; W
J C-1 ; V
A s-1 ; C
The potential difference between two points could be defined as the ratio of which two quantities?
Power dissipated and current
Voltage and resistance
Current and resistance
Charge and time
The potential difference between two points could be defined as the ratio: currentpower dissipated .
A changing magnetic flux Φ could induce an e.m.f E in a coil given by
E=−dtdΦ
What are the base units of magnetic flux?
m s² A⁻¹
kg m s⁻² A⁻¹
m s⁻¹ A
kg m² s⁻² A⁻¹
The specific heat capacity c of a particular solid, at temperatures close to 0 K, is given by c = aT3 where T is the thermodynamic temperature and a is a constant characteristic of the solid.
Which one of the following gives the SI base units of the constant a?
kg m² s⁻² K⁻⁴
kg m² s⁻² K⁻³
m² s⁻² K⁻⁴
m² s⁻² K⁻³
The heat capacity C of a solid as a function of its temperature T is given by the expression
C = αT + βT3
Which row in the table shows possible units of α and β?
A
B
C
D
The diameter d of a uniform wire was measured using a micrometer, reading to ±0.01 mm, and the following results were obtained:
1.02 mm 1.02 mm 1.01 mm 1.02 mm 1.02 mm
The micrometer gives a reading of -0.02 mm when the wire is removed and the jaws are closed. At the appropriate precision, what is the value of d?
1.0 mm
1.00 mm
1.038 mm
1.04 mm
Which of the following shows the speed of sound with the appropriate number of significant figures if calculated to be 327.66 m s⁻¹ with an accuracy of ±3%?
300 m s⁻¹
327.7 m s⁻¹
328 m s⁻¹
330 m s⁻¹
Which one of the following will involve random errors in the measurement?
Not allowing for zero error on a moving-coil voltmeter
Not subtracting background count rate when determining the count rate from a radioactive source
Stopping a stopwatch at the end of a race
Using the value of g as 10 N kg⁻¹ when calculating weight from mass
What is the most appropriate way for the student to report the diameter of the wire measured as 1.52 mm, 1.48 mm, 1.49 mm, 1.51 mm, and 1.49 mm?
(1.50 ± 0.01) mm
1.5 mm
(1.498 ± 0.012) mm
1.498 mm
Several pairs of readings are plotted on a graph and the gradient of the best-fit line is used to determine the measurand. Which of the following statements about this method is incorrect?
It reduces the effects of random errors.
It may be possible to identify 'poor' readings.
It may be possible to identify and avoid random errors.
It may be possible to identify and avoid systematic errors.
The diameter of a steel ball was determined by using a metre rule to measure four similar balls in a row. The positions on the scale were estimated to be as follows: X (1.0 ± 0.2) cm, Y (5.0 ± 0.2) cm. Which of the following gives the value of the diameter with its associated uncertainty?
(1.0 ± 0.05) cm
(1.0 ± 0.1) cm
(1.0 ± 0.2) cm
(1.0 ± 0.24) cm
In an experiment, the time t for a ball to fall from rest through a vertical distance h was measured. The given graph was plotted by a student who knew that the equation h = ½ g t² applies. Which statement is an explanation for the intercept?
Air resistance should be taken into account for larger values of h.
There is a constant delay between starting the timer and releasing the ball.
There is an error in the timer which consistently makes it run fast.
The student should have plotted h against t².
Which one of the following techniques could reduce or eliminate the systematic error of the quantity being measured?
Adjusting an ammeter to remove its zero error before measuring a current.
Measuring several internodal distances on a standing wave to find the mean internodal distance.
Measuring the diameter of a wire repeatedly and calculating the average.
Timing a large number of oscillations to find a period.
Four balances were used to measure the mass of a 1.000 kg weight. The reading was taken five times at each balance. The values obtained and the means are shown in the given table. Which balance is not very precise but has the smallest systematic error?
Balance A
Balance B
Balance C
Balance D
In an experiment to measure the acceleration of free fall g, each of four students made a series of measurements. The results are as shown in the given table. Which of the students obtained results that could be considered precise but not accurate?
Student A
Student B
Student C
Student D
Systematic and random errors may be compared by contrasting the following pairs of properties:
P1: error can possibly be eliminated
P2: error cannot possibly be eliminated
Q1: error is of constant sign and magnitude
Q2: error is of varying sign and magnitude
R1: error will be reduced by averaging repeated measurements
R2: error will not be reduced by averaging repeated measurements
What are the properties applicable to random errors?
P₁, Q₁, R₂
P₁, Q₂, R₂
P₂, Q₂, R₁
P₂, Q₁, R₁
The true value of a quantity x is x₀. In an experiment, the quantity is measured many times and the number N of readings giving a value x is plotted against x. Which of the following graphs best shows measurements that are precise but not accurate?
Graph A
Graph B
Graph C
Graph D
The power loss P in a resistor can be calculated by measuring the potential difference V and the resistance R, and using the equation P = V²/R. In the experiment, the uncertainty in V and R was estimated to be 3% and 2% respectively. What is the uncertainty in the calculated value of P?
4%
7%
8%
11%
The acceleration of free fall g was to be determined by measuring the period of oscillation T and the length l of a simple pendulum, and using the formula g = 4π²l/T².
In the experiment, the uncertainties in measuring l and T were estimated to be 4% and 1% respectively. What is the uncertainty in g?
2%
3%
5%
6%
The volume of a cube was determined by measuring its dimensions with vernier callipers, which can be read with an uncertainty of ±0.1 mm. The length of each side was measured as 30 mm. What is the approximate uncertainty in the value of its volume?
271 %
103 %
31 %
1 %
A resistor is marked as having a value of 4.7 Ω ± 2%. The power P dissipated in the resistor, when connected in a simple electrical circuit, was to be calculated from the current in the resistor, which measured as (2.50 ± 0.05) mA. What is the percentage uncertainty in the calculated value of P?
2%
4%
6%
8%
The sides of a rectangular wafer of silicon were measured using vernier callipers to the nearest tenth of a millimetre. The lengths measured by a student were 10.4 mm, 6.3 mm and 2.3 mm. Which of the following gives the volume of the wafer with the appropriate precision?
1.5070×102 mm3
1.507×102 mm3
1.51×102 mm3
1.5×102 mm3
The mass and linear dimensions of a rectangular block were measured and the results obtained, and their associated uncertainties, are given in the table.
The density of the block was calculated to be 2.50 g cm-3. What was the uncertainty in the calculated density?
± 0.01 g cm-3
± 0.02 g cm-3
± 0.05 g cm-3
± 0.13 g cm-3
The given table shows the data measured by a student to calculate the Young modulus for a brass which was in the form of a wire.
Which of the following contributes most to the uncertainty in the calculated value of the Young modulus?
measurement of length
measurement of diameter
measurement of load
measurement of extension
The velocity v of a liquid in a pipe was to be determined by measuring the force F on a small disc placed in the centre of the pipe with its plane perpendicular to the flow. The equation relating F to v is
F=kv2
where k is a constant.
The velocity v had to be calculated with a maximum uncertainty of 1%. What is the maximum permissible uncertainty in measuring the force F?
0.25%
0.5%
1%
2%
Which one of the following is not a vector quantity?
acceleration
mass
momentum
velocity
Which one of the following pairs comprises one vector quantity and one scalar quantity?
displacement : acceleration
force : kinetic energy
momentum : velocity
power : speed
Which list of quantities contains only scalar quantities?
mass, acceleration, temperature, kinetic energy
mass, volume, electric potential, kinetic energy
acceleration, temperature, volume, electric charge
moment, electric field, density, magnetic flux
Which one of the following pairs comprises one scalar quantity and one vector quantity?
kinetic energy and momentum
potential energy and work
velocity and acceleration
weight and force
Which one of the following lists has the quantities force, kinetic energy, and momentum correctly identified as scalar or vector?
scalar, scalar, scalar
scalar, vector, vector
vector, scalar, scalar
vector, scalar, vector
Fig. 1 shows the directions and lines of action of two forces applied to a circular disc. Which one of the arrows in Fig. 2 best represents the line of action of the resultant force?
A
B
C
D
The given diagram shows the directions of three co-planar forces, of magnitudes 20 N, 40 N, and 50 N, applied to a particle at P. What is the approximate bearing of the additional force required to maintain equilibrium?
37°
127°
143°
217°
Two forces of magnitudes 4 N and 6 N are applied to a point. Which one of the following could not be the magnitude of their resultant?
1 N
4 N
8 N
10 N
The given diagram shows a particle with an initial velocity of 15 m s⁻¹ in the Ox direction. Its velocity, at a later time, is 15 m s⁻¹ at an angle of 60° to Ox. What change of velocity has taken place in this interval?
Zero
26 m s⁻¹ at an angle of 30° to Ox
15 m s⁻¹ at an angle of 120° to Ox
15 m s⁻¹ at an angle of 360° to Ox
Three forces of magnitudes 5 N, 4 N, and 3 N are in equilibrium. Assuming that sin 37° = 0.6, what is the angle between the 5 N force and the 3 N force?
37°
53°
90°
127°
Ben, Sam, and Jim are pushing a large object. Ben exerts a force of 400 N at 60° to Ox while Sam exerts a force of 200 N at a direction of 30° to Ox. Which one of the following sketches shows the magnitude and direction of the smallest force that Jim should exert such that the resultant of the three forces acts along Ox?
Jim 492 N at 30°
Jim 200 N at 0°
Jim 246 N at 90°
Jim 284 N at 60°
The given diagram shows a horizontal force F applied to a body of mass m on a smooth plane inclined at an angle θ to the horizontal. What is the magnitude of the resultant force acting on the body?
F cos θ - mg sin θ
F sin θ + mg cos θ
F sin θ - mg cos θ
F cos θ + mg sin θ
On a smooth horizontal surface, a body of mass 2 kg is moving with a speed of 1.41 m s⁻¹ in a north-easterly direction, when a force of 0.2 N acting in a westerly direction is applied to the body for 10 s. What is the resultant speed of the body?
0.41 m s⁻¹ in a north-easterly direction
1.00 m s⁻¹ in a northerly direction
1.41 m s⁻¹ in a north-westerly direction
2.24 m s⁻¹ in a direction 63.4° east of north
