Which two quantities have the base unit kg m² s⁻²? A kinetic energy and momentum B kinetic energy and Young modulus C work done and the moment of a couple D work done and pressure - AQA - A-Level Physics - Question 7 - 2022 - Paper 1

To determine which quantities have the base unit kg m² s⁻², we analyze the units of each option:

• Kinetic Energy (KE) is defined as: $KE = \frac{1}{2}mv^2$ The unit is Joules (J), which can be expressed in base units as kg m² s⁻².

• Momentum (p) is defined as: $p = mv$ The unit is kg m/s.

This means that option A does not consist of two quantities that share the same unit.

• Young Modulus has units of pressure (force per area), which is N/m² or kg m⁻¹ s⁻², hence option B is also excluded.

• Work Done (W) is given by: $W = F imes d$ The unit is also Joules (kg m² s⁻²), which corroborates the first part of option C.

• The Moment of a Couple has units of N·m (Newton meters), which is equivalent to kg m² s⁻².

Thus, option C is correct as both 'work done' and 'the moment of a couple' share the base unit kg m² s⁻².