Not given in the exam, recall it.
What it is for
Newton's universal law of gravitation is used in Gravitation (SPM Physics Form 4). Keep the SI units in every line of working. Gravitation
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| F | gravitational force | N |
| G | gravitational constant | N m² kg⁻² |
| m₁ | mass of first object | kg |
| m₂ | mass of second object | kg |
| r | distance between centres | m |
Rearrangements
m₁ = Fr² / (G m₂)r = √(G m₁m₂ / F)
Worked example
Common trap
Understanding Newton's universal law of gravitation
Newton’s law states that every pair of masses attracts each other with a force F = G m₁m₂ / r².
Here F is the gravitational force in newtons (N), G is the gravitational constant, 6.67 × 10⁻¹¹ N m² kg⁻², m₁ and m₂ are the two masses in kilograms (kg), and r is the distance between their centres in metres (m). The force grows with either mass but falls off as the square of the distance, so doubling r quarters the force.
To find one mass, rearrange to m₁ = Fr² / (G m₂); to find the separation, use r = √(G m₁m₂ / F). The same pull acts on both masses, in opposite directions.
A worked example, step by step
Two dense spheres of mass m₁ = 1000 kg and m₂ = 2000 kg have their centres r = 5 m apart. Take G = 6.67 × 10⁻¹¹ N m² kg⁻².
Find the gravitational force between them.
Write the formula and substitute with units:
F = G m₁m₂ / r² = (6.67 × 10⁻¹¹ N m² kg⁻² × 1000 kg × 2000 kg) / (5 m)²
F = (1.334 × 10⁻⁴) / 25 = 5.34 × 10⁻⁶ N.
The force is tiny even for tonnes of mass a few metres apart, which is why gravitation between everyday objects is never noticed. The answer is quoted to three significant figures with the newton.
Common mistakes and how this is tested
The most important rule is that r is the distance between the centres of the objects and it must be squared; forgetting the square is the classic error.
Other mistakes: dropping the constant G or misreading its power of ten (6.67 × 10⁻¹¹); measuring r from the surfaces instead of the centres; and mishandling standard form when multiplying the small and large numbers.
This is tested under define (state the law in words), calculate (find F, a mass, or r), and explain (why the force weakens rapidly with distance, or why we do not feel the pull between two people).
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)