2018 A/L Physics Past Paper · Question 01 (English Medium)

Answer: (3) kg m⁻¹ s⁻²

What the question asks

Write the unit of pressure using only kg, m and s.

Then find the option that matches.

Relevant theory

Pressure is defined as the force on a unit area of a surfaces, normal to that surface.

The S.I. unit of pressure is N m^-2 and this unit is known as "pascal" (Pa).

Pressure is force divided by area.

$$p = \frac{F}{A}$$

The unit of force is $kg\,m\,s^{-2}$.

The unit of area is $m^{2}$.

So the dimensions of pressure are $[M\,L^{-1}\,T^{-2}]$.

Reading the options

Each option is set beside the dimensions of pressure.

asked

M L^{-1} T^{-2}

$p = F/A$

1

M L T^{-2}

$kg m s^{-2}$

2

M L^2 T^{-2}

$kg m^2 s^{-2}$

3

$kg m^{-1} s^{-2}$

4

M L^2 T^{-3}

$kg m^2 s^{-3}$

5

M L^{-2} T^{-2} I^{-1}

$kg m^{-2} s^{-2} A^{-1}$

Option (1) is the unit of force.

Option (2) is the unit of energy. Option (4) is the unit of power.

Option (5) has A, the unit of current. Pressure has nothing to do with current.

None of these four is $[M\,L^{-1}\,T^{-2}]$.

Checks

Check the dimensions.

$$[p] = \frac{M\,L\,T^{-2}}{L^{2}} = M\,L^{-1}\,T^{-2}$$

Option (3) has the same dimensions.

Check the unit too. The SI unit of pressure is $N\,m^{-2}$ (the pascal).

$$N\,m^{-2} = kg\,m\,s^{-2} \times m^{-2} = kg\,m^{-1}\,s^{-2}$$

This is option (3).

Conclusion

$\text{Pa} = \text{kg m}^{-1}\text{s}^{-2}$

The unit of pressure is

$$kg\,m^{-1}\,s^{-2}$$

The answer is (3).

In a unit question, first write the equation that defines the quantity.

$$p = \frac{F}{A}$$

Then change every unit into kg, m and s.

Exam tip