WorksheetsUncertainties & Errors - Part 1
Total questions: 30
Worksheet time: 3hrs 30mins
A
B
C
D
A
B
C
D
2%
5%
7%
10%
0.25%
5%
10%
25%
8%
12%
14%
20%
The first length measured in a laboratory experiment is 2.5 + 0.1 m and the second length 3.4 + 0.1 m. What is the uncertainty of the sum of the lengths?
0.1 m
0.2 m
0.3 m
0.4 m
The first length measured in a laboratory experiment is 2.5 + 0.1 m and the second length 3.4 + 0.1 m. What is the uncertainty of the difference in the lengths?
0.1 m
0.2 m
0.3 m
0.4 m
State the order of magnitude of the following: 0.000656
10 -4
10 -3
10 -2
10 -1
State the order of magnitude of the following: 539
600
500
10 3
10 2
A pile of sand has a width that ranges from 38 m to 41 m and a length that is approximately 125 m. If the depth varies from 8.8 m to 9.1 m, what is the order of magnitude of the volume ?
10 4
10 3
10 2
10 1
Solve and state the order of magnitude in SI unit:
81 nm + 96 cm + 21 pm + 148 mm
10 4
10 3
10 2
10 1
A number rounded to the nearest power of 10 is called:
Estimation
Orders of magnitude
Metric multipliers
Prefixes
True or False?
Repeating a reading never removes the systematic error.
True
False
True or False?
When measuring a time manually it is inappropriate to use the precision of the digital timer as the uncertainty in a reading.
True
False
A student measures the acceleration due to gravity as 9.0m/s2 ±10%. Is this answer valid within the experimental uncertainty?
Yes
No
The resistance R of a resistor is determined by measuring the potential difference V across it and the current I in it. The value of R is then calculated using the equation
R=IV .
The values measured are V = 1.00 ± 0.05 V and I = 0.50 ± 0.01 A. What is the % uncertainty in the value of R?
2.5 %
3.0 %
7.0 %
10.0 %
In an experiment, a radio-controlled car takes 2.50 ± 0.05 s to travel 40.0 ± 0.1 m.
What is the car’s average speed and the uncertainty in this value?
16 ± 1m s-1
16.0 ± 0.2 m s-1
16.0 ± 0.4 m s-1
16.00 ± 0.36 m s-1
In an experiment to determine the acceleration of free fall g, the period of oscillation T and length l of a simple pendulum were measured. The uncertainty in the measurement of l is estimated to be 4%, and the uncertainty in the measurement of T is estimated to be 1%.
The value of g is determined using the formula g=T24π2l
What is the uncertainty in the calculated value for g?
2 %
3 %
5 %
6 %
An experiment is carried out to measure the resistance of a wire.
The current in the wire is (1.0 ± 0.2) A and the potential difference across the wire is (8.0 ± 0.4) V.
What is the resistance of the wire and its uncertainty?
(8.0 ± 0.2) Ω
(8.0 ± 0.6) Ω
(8 ± 1) Ω
(8 ± 2) Ω
A thermometer can be read to an accuracy of ±0.5 °C. This thermometer is used to measure a temperature rise from 40 °C to 100 °C.
What is the percentage uncertainty in the measurement of the temperature rise?
0.5 %
0.8 %
1.3 %
1.7 %
A digital caliper is used to measure the 28.50 mm width of a plastic ruler. The digital caliper reads to the nearest 0.01 mm.
What is the correct way to record this reading?
0.02850 ± 0.01 m
0.0285 ± 0.001 m
(2.850 ± 0.001) × 10-2 m
(2.850 ± 0.001) × 10-3 m
A student determines the density ρ of steel by taking measurements from a steel wire.
mass m = 6.2 ± 0.1 g
length l = 25.0 ± 0.1cm
diameter d = 2.00 ± 0.01mm
He uses the equation ρ=πd2l4m .
What is the percentage uncertainty in his calculated value of density?
1.1 %
1.8 %
2.5 %
3.0 %
A quantity x is to be determined from the equation
x = P-Q.
P is measured as 1.27 ± 0.02 m and Q is measured as 0.83 ± 0.01 m.
What is the percentage uncertainty in x to one significant figure?
0.4 %
2 %
3 %
7 %
The measurement of a physical quantity may be subject to random errors and to systematic errors.
Which statement is correct?
Random errors can be reduced by taking the average of several measurements.
Random errors are always caused by the person taking the measurement.
A systematic error cannot be reduced by adjusting the apparatus.
A systematic error results in a different reading each time the measurement is taken.
A micrometer screw gauge is used to measure the diameter of a small uniform steel sphere. The micrometer reading is 5.00mm ± 0.01mm.
What will be the percentage uncertainty in a calculation of the volume of the sphere, using these values?
0.2 %
0.4 %
0.6 %
1.2 %
What could reduce systematic errors?
averaging a large number of measurements
careful calibration of measuring instruments
reducing the sample size
repeating measurements
The power loss P in a resistor is usually calculated using the formula P=RV2
The percentage uncertainty in the potential difference V is 3 % and the percentage uncertainty in the resistance R is 2 %. What is the percentage uncertainty in P?
4 %
7 %
8 %
11 %
The sides of a wooden block are measured with calipers. The lengths of the sides are measured as 20.0 mm, 40.0 mm and 10.0 mm.
The calipers can measure with an absolute uncertainty of ± 0.1 mm. What is the percentage uncertainty in the calculated volume of the block?
0.3 %
1.8 %
3.8 %
30 %
The width of a table is measured as (50.3 ± 0.1) cm. Its length is measured as (1.40 ± 0.01) m.
What is the area of the table and its absolute uncertainty?
(0.7 ± 0.1) m2
(0.704 ± 0.006) m2
(0.704 ± 0.011) m2
(70.4 ± 0.6) m2
A steel wire is stretched in an experiment to determine the Young modulus for steel.
The uncertainties in the measurements are given in the table.
What is the percentage uncertainty in the Young modulus?
1.3 %
1.8 %
4.7 %
6.2 %
