5 When a sphere of radius \(r\) metres is falling at \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) it experiences an air resistance force \(F\) newtons.
The force is to be modelled as
$$F = k r ^ { \alpha } { } _ { V } { } ^ { \beta }$$
where \(k\) is a constant with units \(\mathrm { kg } \mathrm { m } ^ { - 2 }\)
5
- State the dimensions of \(F\)
5 - Use dimensional analysis to find the value of \(\alpha\) and the value of \(\beta\)