Unit 1 - Uncertainty

A student wants to determine the angular speed ω of a rotating object. The period T is 0.50 s ±5 %. The angular speed ω is ω=2πT

What is the percentage uncertainty of ω?

• 0.2 %

• 2.5 %

• 5 %

• 10 %

A student measures the radius R of a circular plate to determine its area. The absolute uncertainty in R is ΔR.

What is the fractional uncertainty in the area of the plate?

• 2ΔR/R

• (ΔR/R)²

• 2πΔR/R

• π(ΔR/R)²

A student is verifying the equation

x=2λY/z

The percentage uncertainties are shown in the picture

What is the percentage uncertainty in x?

• 5 %

• 15 %

• 25 %

• 30 %

The length of the side of a cube is 2.0 cm ± 4 %. The mass of the cube is 24.0 g ± 8 %. What is the percentage uncertainty of the density of the cube?

• ± 2 %

• ± 8 %

• ± 12 %

• ± 20 %

A student measures the radius r of a sphere with an absolute uncertainty Δr. What is the fractional uncertainty in the volume of the sphere?

• (Δr/r)³

• 3Δr/r

• 4πΔr/r

• 4π(Δr/r)3

An object is positioned in a gravitational field. The measurement of gravitational force acting on the object has an uncertainty of 3 % and the uncertainty in the mass of the object is 9 %. What is the uncertainty in the gravitational field strength of the field? (Force = mass x field strength)

• 3 %

• 6 %

• 12 %

• 27 %

A stone falls from rest to the bottom of a water well of depth d. The time t taken to fall is 2.0 ±0.2 s. The depth of the well is calculated to be 20 m using d = A stone falls from rest to the bottom of a water well of depth d. The time t taken to fall is 2.0 ±0.2 s. The depth of the well is calculated to be 20 m using  $d=\frac{1}{2}at^2$ . The uncertainty in a is negligible. What is the absolute uncertainty in d?

• ± 0.2 m

• ± 1 m

• ± 2 m

• ± 4 m

The graph shows a set of experimental results to determine the density of oil. The results have systematic errors and random errors.

Using the information on the graph, what can be said about the measurements used to find the density of oil?

• Systematic: small Random: small

• Systematic: small Random: large

• Systematic: large Random: small

• Systematic: large Random: large

The volume V of a cylinder of radius R and height H is given by V = πR²H. The volume of the cylinder was measured with an uncertainty of 10% and the height was measured with an uncertainty of 6%. What is the uncertainty in the radius of the cylinder?

• 1%

• 2%

• 4%

• 8%

The masses and weights of different objects are independently measured. The graph is a plot of weight versus mass that includes error bars.

• measurements show a significant systematic error but small random error.

• measurements show a significant random error but small systematic error.

• measurements are precise but not accurate.

• weight of an object is proportional to its mass.