Errors and measurement of physical quantities

1. In an experiment, a radio-controlled car takes 2.50 ± 0.05s to travel 40.0 ± 0.1m.

What is the car’s average speed and the uncertainty in this value?

• 16 ± 1ms-1

• 16.0 ± 0.2ms-1

• 16.0 ± 0.4ms-1

• 16.00 ± 0.36ms^-1

A mass is dropped from rest, and falls through a distance of 2.0m in a vacuum. An observer records the time taken for the mass to fall through this distance using a manually operated stopwatch and repeats the measurements a further two times. The average result of these measured times, displayed in the table below, was used to determine a value for the acceleration of free fall. This was calculated to be 9.8ms^-2.

Which statement best relates to the experiment?

• The measurements are precise and accurate with no evidence of random errors.

• The measurements are not accurate and not always recorded to the degree of precision of the measuring device but the calculated experimental result is accurate.

• The measurements are not always recorded to the degree of precision of the measuring device but are accurate. Systematic errors may be present.

• The range of results shows that there were random errors made but the calculated value is correct so the experiment was successful.

Variables x and y are related by the equation y = p– qx where p and q are constants. Values of x and y are measured experimentally. The results contain a systematic error. Which graph best represents these results?

• A

• B

• C

• D

The speed of a car is calculated from measurements of the distance travelled and the time taken. The distance is measured as 200m, with an uncertainty of ±2m. The time is measured as 10.0s, with an uncertainty of ±0.2s. What is the percentage uncertainty in the calculated speed?

• ±0.5%

• ±1%

• ±2%

• ±3%

In an experiment to determine the acceleration of free fall g, the time t taken for a ball to fall through distance s was measured. The uncertainty in the measurement of s is estimated to be 2%. The uncertainty in the measurement of t is estimated to be 3%. The value of g is determined using the equation:

 $g=\frac{2s}{t^2}$ 

 What is the uncertainty in the calculated value of g?

• 1%

• 5% 

• 8% 

• 11%

Which experimental technique reduces the systematic error of the quantity being investigated?

• adjusting an ammeter to remove its zero error before measuring a current

• measuring several internodal distances on a standing wave to find the mean intermodal distance

• measuring the diameter of a wire repeatedly and calculating the average

• timing a large number of oscillations to find a period.

A force of 5 N may be represented by two perpendicular components OY and OX as shown in the diagram, which is not drawn to scale. OY is of magnitude 3 N. What is the magnitude of OX?

• 2N

• 3N

• 4N

• 5N

Four students each made a series of measurements of the free fall g. The table shows the results obtained. Which set of results could be described as precise but not accurate?

• А

• В

• С

• D

Four different students use a ruler to measure the length of a 15.0cm pencil. Their measurements are recorded on four different charts. Which chart shows measurements that are precise but not accurate?

• A

• B

• C

• D

The density of the material of a coil of thin wire is to be found. Which set of instruments could be used to do this most accurately?

• metre rule, protractor, spring balance

• micrometer, metre rule, top-pan balance

• stopwatch, newton-meter, vernier calipers

• tape measure, vernier calipers, lever balance