Derived Units & Homogeneity
The trolley's distance is measured in metres and its time is measured in seconds. Therefore the calculated speed has the unit:
These examples use relations taught later in the course. At this point, a question may supply the relation; focus on replacing each quantity with its base units.
Express the ohm in SI base units. Use resistance = potential difference ÷ current and potential difference = power ÷ current.
The units match, so the equation passes the homogeneity check. This does not prove that the numerical factor or physical model is correct.
A mass hangs on a spring with spring constant . Test whether is homogeneous.