Question

The following equations for force were re- written in terms of only base dimensions, with the exception of an unknown parameter, k. Determine the required dimensions of k to make the equation dimensionally consistent.


`mL^2L^(-1)t^2=kL^2t^4`

Answer 1

m/(Lt²)

Explanation:

To find the dimensions of k, divide by its coefficient.

`mL^2L^(-1)t^2 = kL^2t^4\qquad\text{given}\\\\(mL^2L^(-1)t^2)/(L^2t^4)=k\qquad\text{divide by $L^2t^4$}\\\\k=(mL^(-1))/(t^2)\qquad\text{cancel common factors}`

The dimensions of k are m/(Lt²).