The correct answer is C because:

The units of the variables are:
- g : m s⁻²
- r : m
- ⍴ : kg m⁻³
- ɳ : kg m⁻¹ s⁻¹
Substituting these units into the equation and ignoring constants:
- $m s^{- 1} = \frac{(m s^{- 2}) (m^{n}) ({kgm}^{- 3})}{kg m^{- 1} s^{- 1}}$
- $m s^{- 1} = \frac{m^{- 2} s^{- 2} m^{n} kg}{kg m^{- 1} s^{- 1}}$
- $m s^{- 1} = m^{- 1} s^{- 1} m^{n}$

For the sides to balance n must be 2 so that:
- $m s^{- 1} = m^{- 1} s^{- 1} m^{2}$
- $m s^{- 1} = m s^{- 1}$

A is incorrect because:

$m s^{- 1} = \frac{(m s^{- 2}) (m^{\frac{1}{2}}) (kg m^{- 3})}{kg m^{- 1} s^{- 1}}$
$m s^{- 1} = m^{- 1} s^{- 1} m^{\frac{1}{2}}$
$m s^{- 1} = m^{- \frac{1}{2}} s^{- 1}$

B is incorrect because:

$m s^{- 1} = \frac{(m s^{- 2}) (m) (kg m^{- 3})}{kg m^{- 1} s^{- 1}}$
$m s^{- 1} = m^{- 1} s^{- 1} m$
$m s^{- 1} = s^{- 1}$

D is incorrect because:

$m s^{- 1} = \frac{(m s^{- 2}) (m^{3}) (kg m^{- 3})}{kg m^{- 1} s^{- 1}}$
$m s^{- 1} = m^{- 1} s^{- 1} m^{3}$
$m s^{- 1} = m^{2} s^{- 1}$

Make sure to substitute the units of all of the terms into the equations. Then set n such that the equation is homogeneous. An equation is homogeneous when the units on both sides of the equation are the same.

SI Units (CIE A Level Physics)

Exam Questions