A sphere fits inside a cube.
The length of the cube and the diameter of the sphere are .
What is the ratio
A proton is confined within a nucleus. What is the order of magnitude of the uncertainty in its momentum?
A chain is suspended between two vertical supports A and The chain is made of a number of identical metal links.
The length l of the chain can be increased by adding extra links. An experiment was undertaken to investigate how the sag d of the midpoint of the chain, measured from the horizontal between A and B, varies with l. The data obtained are shown plotted below. The uncertainties in l are too small to be shown.
Estimate the horizontal distance between the supports A and B.
Explain why the relationship between d and l is not linear.
Draw a best-fit line for the data points on the graph opposite.
Before the experiment was carried out, it was hypothesized that d depends on √l. Determine, using your answer to , whether this hypothesis is valid.
A stone falls from rest to the bottom of a water well of depth . The time taken to fall is . The depth of the well is calculated to be 20 m using . The uncertainty in is negligible.
What is the absolute uncertainty in ?
A radio wave of wavelength λ is incident on a conductor. The graph shows the variation with wavelength λ of the maximum distance d travelled inside the conductor.
Suggest why it is unlikely that the relation between d and λ is linear.
For λ = 5.0 × 10^5 m, calculate the fractional uncertainty in d.
For λ = 5.0 × 10^5 m, calculate the percentage uncertainty in d^2.
The graph shows the variation with wavelength λ of d^2. Error bars are not shown and the line of best-fit has been drawn.
A student states that the equation of the line of best-fit is d^2 = a + bλ. When d^2 and λ are expressed in terms of fundamental SI units, the student finds that a = 0.040 × 10^-4 and b = 1.8 × 10^-11
State the fundamental SI unit of the constant a and of the constant b.
Determine the distance travelled inside the conductor by very high frequency electromagnetic waves.
The kilowatt-hour is equivalent to approximately
A student is verifying the equation The percentage uncertainties are:
Quantity | Uncertainty |
---|---|
What is the percentage uncertainty in x?
Which of the following expresses the ratio as a difference in orders of magnitude?
An object is positioned in a gravitational field. The measurement of gravitational force acting on the object has an uncertainty of and the uncertainty in the mass of the object is . What is the uncertainty in the gravitational field strength of the field?
The radius of a sphere is measured with an uncertainty of . What is the uncertainty in the volume of the sphere?