When do mass and weight get confused?

Mass is in kilograms and does not change, while weight is in newtons and follows g; force problems always use mass.

Is there a shortcut for ratio questions?

Write the new radius as a multiple, square it and invert, and the force ratio appears without G or the masses.

S6 Physics Gravitation, Paper 4: mixed calculation and working backwards

2026-11-02

Tutor Prep Guide · Primary English

Ten graded items from weight and the inverse square law through orbital period and escape speed to Kepler ratios.

Focus　Keep weight as mg and attraction as G m one m two over r squared apart, and square the distance ratio before inverting it.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S6 Physics: Gravitation
Level	Four basic, three advanced, two challenge and one error-repair item

02　Questions (10 items)

FoundationFind the weight of a 20 kg student on Earth, with g as 9.8 m/s^2.
FoundationTwo 3 kg spheres sit 0.3 m apart. Find the gravitational force between them.
FoundationThe same 70 kg astronaut stands on Mars where g is 3.7 m/s^2. Find the new weight.
FoundationIf the separation between two masses grows to five times, what fraction of the force remains?
IntermediateWith Earth mass 6.0 x 10^24 kg and radius 6.4 x 10^6 m, find g at the surface.
IntermediateA satellite circles at r = 4.2 x 10^7 m. Find its period in seconds and in hours.
IntermediateA planet has radius 3.0 x 10^6 m and surface g of 3.7 m/s^2. Find its escape speed in km/s.
ChallengeAt a height of twice Earth radius, so r = 3R, what fraction of surface g remains, and what is the value?
ChallengeTwo satellites orbit one planet and the outer period is three times the inner one. Find the radius ratio.
Error redoA student says g is still 9.8 m/s^2 at a height equal to Earth radius. Give the correct value.

03　Answers and one-line notes

#	Answer	One-line note
1	196 N	Weight is mass times g, so 20 times 9.8 gives 196 N.
2	6.67 x 10^-9 N	Six point six seven times ten to the minus eleventh times nine divided by 0.09 gives about 6.67 x 10^-9 N.
3	259 N	Seventy kilograms times 3.7 gives 259 N while the mass stays at 70 kg.
4	One twenty-fifth	The force falls with the square of distance, so five times the separation leaves one twenty-fifth.
5	9.77 m/s^2	GM over R squared gives 9.77 metres per second squared, close to the accepted 9.8.
6	About 8.5 x 10^4 s, that is 23.7 hours	The period comes out near 8.5 x 10^4 s, about 23.7 hours, close to a geostationary orbit.
7	About 4.71 km/s	Root two g R gives about 4 712 metres per second, or 4.71 kilometres per second.
8	One ninth, about 1.09 m/s^2	Tripling the distance cuts g to one ninth, so 9.8 divided by 9 is about 1.09.
9	About 2.08 times	Since period squared scales with radius cubed, the radius grows as T to the two thirds, giving about 2.08.
10	2.45 m/s^2	At height R the distance is 2R, so g drops to a quarter, giving 2.45; 9.8 only holds near the surface.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

Book an S6 Physics tutor Tutor Registration →

Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.