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

Answer:

  m/(Lt²)

Step-by-step explanation:

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

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

The dimensions of k are m/(Lt²).