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9702 · 1.2

SI units — practice questions

Practice and worked examples for 9702 SI units. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

The period T of a simple pendulum is thought to depend on its length l and the acceleration of free fall g. The proposed equation is T = 2π√(l/g). Use dimensional analysis to show that this equation is homogeneous.

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  1. Identify the base units for each side of the equation.
    • LHS (Left Hand Side): The quantity is period T, which is a time. Its SI base unit is seconds (s).
    • RHS (Right Hand Side): The equation involves length l (unit: m) and acceleration g (unit: m s⁻²). The term 2π is a dimensionless constant and has no units.
  2. Analyse the units of the LHS.
    • [LHS] = [T] = s
  3. Analyse the units of the RHS.
    • [RHS] = [√(l/g)]
    • Substitute the units: [RHS] = √(m / (m s⁻²))
  4. Simplify the units on the RHS.
    • [RHS] = √(m × s² / m)
    • The 'm' units cancel out: [RHS] = √(s²)
    • [RHS] = s
  5. Compare LHS and RHS.
    • [LHS] = s and [RHS] = s.
    • Since the base units on both sides are identical, the equation is dimensionally homogeneous.

Worked example 2

A radio station broadcasts at a frequency of 98.4 MHz. Convert this frequency to hertz (Hz). A capacitor has a capacitance of 250 pF. Convert this to farads (F).

Show solution outline
  1. For 98.4 MHz to Hz: The prefix 'Mega' (M) means 10⁶. So, 98.4 MHz = 98.4 × 10⁶ Hz = 98,400,000 Hz.
  2. For 250 pF to F: The prefix 'pico' (p) means 10⁻¹². So, 250 pF = 250 × 10⁻¹² F = 2.5 × 10⁻¹⁰ F.
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