PhysicsICSE Class 9 · Gravitation

Mass, Weight and Acceleration Due to Gravity: W = mg and g = GM/R² (ICSE Class 9)

Updated 17 October 2026 · Fact-checked

Mass is the quantity of matter in a body (kg, constant everywhere). Weight W = mg is the force with which a planet pulls the body (N, changes with g). The acceleration due to gravity at a planet’s surface is g = GM/R², independent of the falling body’s mass. 1 kgf = 9.8 N and 1 gf = 980 dyne.

Notice that the mass stays 10 kg on both worlds, but the weight W = mg shrinks on the Moon because g is smaller.

Illustration drawn for QuestionBuddy.

Understand Mass, Weight and Acceleration Due to Gravity (g)

Acceleration due to gravity. When a body is allowed to fall with only gravity acting (free fall), its velocity increases by $g$ every second. Near the Earth’s surface $g \approx 9.8$ m s⁻² (often taken 10 in numericals). To get an expression for $g$ , equate the weight $m g$ to the gravitational force on a body of mass $m$ at the surface of a planet of mass $M$ and radius $R$ :

$m g = \frac{GM m}{R ^{2}} \Rightarrow g = \frac{GM}{R ^{2}} .$

$m$ cancels: $g$ does not depend on the mass of the falling body, so a heavy and a light body fall together in a vacuum.
$g$ depends on the planet: $g \propto \frac{M}{R ^{2}}$ .

Comparing planets (ratio method). If a planet has mass $a$ times, and radius $b$ times, that of the Earth, then $\frac{g _{p}}{g _{E}} = \frac{a}{b ^{2}}$ . For example $M = 8 M_{E}$ and $R = 2 R_{E}$ gives $g_{p} = 2 g_{E}$ .

Mass. The quantity of matter in a body. Scalar; SI unit kg; the same everywhere; measured with a beam balance by comparing with standard masses.

Weight. The force with which a planet attracts a body: $W = m g$ . Vector, directed to the planet’s centre; SI unit newton; it varies from place to place (and is nearly zero far from all bodies); measured by a spring balance.

	Mass	Weight
Meaning	Matter in the body	Pull of the planet on it
Nature	Scalar	Vector (force)
SI unit	kg	N
Changes with place?	No	Yes (with $g$ )
Instrument	Beam balance	Spring balance

A beam balance gives the same reading anywhere (the unknown mass and the standard masses are both affected by $g$ equally); a spring balance reads weight and so shows a different value on a planet with another $g$ .

Gravitational units. 1 kgf is the weight of 1 kg: $1 kgf = 9.8$ N. 1 gf is the weight of 1 g: $1 gf = 980$ dyne. A body of mass $m$ kg weighs $m$ kgf. These depend on $g$ , so the newton is preferred in calculations.

Free fall numericals. Use the equations of motion with $a = g$ . On another planet use that planet’s $g$ .

Mass, Weight and Acceleration Due to Gravity (g): formulas and key facts

Acceleration due to gravity: $g = \frac{GM}{R ^{2}}$; Surface value; independent of the falling mass.
Weight: $W = m g$; N; vector.
Planet comparison: $\frac{g _{p}}{g _{E}} = \frac{M _{p}}{M _{E}} \times (\frac{R _{E}}{R _{p}})^{2}$; Ratio method.
Gravitational units: $1 kgf = 9.8 N; 1 gf = 980 dyne$; Weight of 1 kg or 1 g.

How to solve Mass, Weight and Acceleration Due to Gravity (g) questions

Decide whether the question is about mass, weight or g.

1Mass stays the same; only weight changes with g.
2Use $W = m g$ with m in kg to get newtons; divide by 9.8 for kgf.
3For another planet use the ratio $g_{p} / g_{E} = a / b^{2}$ or $g = GM / R^{2}$ .
4For free fall use $h = \frac{1}{2} g t^{2}$ and $v = g t$ with that planet’s g.
5Quote the unit with every answer.

Mass, Weight and Acceleration Due to Gravity (g) in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Weighing luggage on two planets

Suppose a bag has a mass of 20 kg. It is weighed with a spring balance on the Earth and then on a small planet where g is 4.9 m s⁻².

What do the spring balance and a beam balance show in each place?

Try it first, then show the solutionSolution

Earth: $W = 20 \times 9.8 = 196$ N (20 kgf). Small planet: $W = 20 \times 4.9 = 98$ N (10 kgf).
The beam balance reads 20 kg in both places.

Answer: Spring balance 196 N then 98 N; beam balance 20 kg both times.

Memory hook: Spring feels g, beam does not.

Tricks to remember Mass, Weight and Acceleration Due to Gravity (g)

Short memory aids. Say each one aloud once, then use it on a question the same day.

M cancels
In mg = GMm/R² the small m cancels, so g is the same for every falling body.
Use it when: Free-fall reasoning.
Big M up, big R squared down
g goes as M/R². 8 times the mass, twice the radius: 8/4 = 2 times g.
Use it when: Planet ratios.
Weight is a force
Mass in kg, weight in N (or kgf).
Use it when: Unit questions.

Mass, Weight and Acceleration Due to Gravity (g): solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Weight in newtons · 1 mark · MCQBoard level

The weight of a 5 kg body at a place where $g = 9.8$ m s⁻² is:
(a) 5 N
(b) 9.8 N
(c) 49 N
(d) 490 N

Try it first, then show the solutionSolution

$W = m g = 5 \times 9.8 = 49$ N.

Answer: (c) 49 N

Example 2: On a small planet · 2 marks · Short answerBoard level

An astronaut has a mass of 80 kg. On a small planet $g = 4.9$ m s⁻². Find her mass and weight on the planet and her weight on the Earth, in N and kgf.

Try it first, then show the solutionSolution

Mass remains 80 kg. (½)
On the planet $W = 80 \times 4.9 = 392$ N $= \frac{392}{9.8} = 40$ kgf. (1)
On the Earth $W = 80 \times 9.8 = 784$ N $= 80$ kgf. (½)

Answer: 80 kg; 392 N (40 kgf); 784 N (80 kgf)

Example 3: A heavier, larger planet · 3 marks · Short answerHarder board level

A planet has 8 times the mass and twice the radius of the Earth ( $g_{E} = 9.8$ m s⁻²). Find (a) its surface g, (b) the weight of a 50 kg body there, (c) the time a stone takes to fall 39.2 m from rest.

Try it first, then show the solutionSolution

(a) $g_{p} = 9.8 \times \frac{8}{2 ^{2}} = 19.6$ m s⁻². (1)
(b) $W = 50 \times 19.6 = 980$ N. (1)
(c) $t = \frac{2 \times 39.2}{19.6} = 2$ s. (1)

Answer: (a) 19.6 m s⁻² (b) 980 N (c) 2 s

Example 4: Mass fixed, weight not · 3 marks · Short answerHarder board level

A body of mass 12 kg is on the Earth. (a) Find its weight in N. (b) On another planet its weight is 60 N. Find g there and the body’s mass on that planet.

Try it first, then show the solutionSolution

(a) $W = 12 \times 9.8 = 117.6$ N. (1)
(b) $g = \frac{60}{12} = 5$ m s⁻². (1)
Mass is still 12 kg. (1)

Answer: (a) 117.6 N (b) g = 5 m s⁻²; 12 kg

Example 5: Drop test on a planet · 4 marks · Case-basedHOTS / competency

On an unknown planet Z a ball dropped from rest from 20 m takes 4 s to land. Planet Z has radius $3.2 \times 1 0^{6}$ m.
(a) Find g on Z.
(b) Find the landing speed.
(c) A body of mass 8 kg is taken there: find its weight in N and in kgf.
(d) Find the mass of Z ( $G = 6.67 \times 1 0^{- 11}$ ).

Try it first, then show the solutionSolution

(a) $20 = \frac{1}{2} g (16)$ , so $g = 2.5$ m s⁻². (1)
(b) $v = g t = 10$ m s⁻¹. (½)
(c) $W = 8 \times 2.5 = 20$ N $= \frac{20}{9.8} \approx 2.04$ kgf. (1)
(d) $M = \frac{g R ^{2}}{G} = \frac{2.5 \times ( 3.2 \times 1 0 ^{6} ) ^{2}}{6.67 \times 1 0 ^{- 11}} \approx 3.8 \times 1 0^{23}$ kg. (1½)

Answer: (a) 2.5 m s⁻² (b) 10 m s⁻¹ (c) 20 N (2.04 kgf) (d) about 3.8 × 10²³ kg

Where students lose marks in Mass, Weight and Acceleration Due to Gravity (g)

The slips examiners see most often, and what to write instead.

Mistake: Mass changed with place
Mass is the same everywhere.
Wrong working
Mass on the planet = 80 × 4.9/9.8 = 40 kg.
Right working
Mass = 80 kg; weight = 392 N.
Do this: Say "mass unchanged" first.
Usually costs: 1 mark.
Mistake: kgf and kg confused
kg is mass; kgf is force.
Wrong working
Weight = 40 kg
Right working
Weight = 40 kgf (392 N)
Do this: Use f for force units.
Usually costs: The unit mark.
Mistake: Radius ratio not squared
g depends on 1/R².
Wrong working
g ratio = 8/2 = 4
Right working
8/2² = 2
Do this: Write the ratio with the square.
Usually costs: Answer and method.

Exam tips

Write "mass is constant, weight changes" whenever a body is moved to another planet.
Convert N to kgf by dividing by 9.8.
Quote g = GM/R² and state that m cancels when asked why all bodies fall together.
Name the instrument: beam balance for mass, spring balance for weight.

Practice questions on Mass, Weight and Acceleration Due to Gravity (g)

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
The weight of a body is nearly zero:
(a) at the pole of the Earth
(b) deep inside the Earth’s mine
(c) far from all other bodies
(d) on the Moon
Hint
Weight is a pull.
Answer
(c)
Q2 · 1 mark · Very short answerBoard level
State the SI unit of weight.
Hint
It is a force.
Answer
Newton (N).
Q3 · 2 marks · Short answerHarder board level
Express the weight of a 250 g body in dyne ( $g = 980$ cm s⁻²).
Hint
Use cgs units.
Answer
$W = 250 \times 980 = 2.45 \times 1 0^{5}$ dyne (250 gf).
Q4 · 3 marks · Short answerHarder board level
A planet has mass $2.4 \times 1 0^{24}$ kg and radius $3.0 \times 1 0^{6}$ m. Find g on its surface ( $G = 6.67 \times 1 0^{- 11}$ N m² kg⁻²).
Hint
g = GM/R².
Answer
$g = \frac{6.67 \times 1 0 ^{- 11} \times 2.4 \times 1 0 ^{24}}{( 3.0 \times 1 0 ^{6} ) ^{2}} = \frac{1.6 \times 1 0 ^{14}}{9 \times 1 0 ^{12}} \approx 17.8$ m s⁻².
Q5 · 2 marks · Assertion-reasonHarder board level
Assertion (A): A body has the same mass on the Moon as on the Earth but a different weight.
Reason (R): Mass is the quantity of matter, while weight is the gravitational pull on it.
(a) Both true, R explains A.
(b) Both true, R does not explain A.
(c) A true, R false.
(d) A false, R true.
Hint
Different quantities.
Answer
(a)
Q6 · 3 marks · Short answerHOTS / competency
At a certain place a spring balance reads 19.2 N for a standard 2 kg mass. (a) Find g there. (b) Another body reads 4.8 N: find its mass. (c) What would a beam balance show for the 2 kg mass at a place with $g = 9.8$ m s⁻²?
Hint
The first body fixes g.
Answer
(a) $g = \frac{19.2}{2} = 9.6$ m s⁻². (b) $m = \frac{4.8}{9.6} = 0.5$ kg. (c) 2 kg: a beam balance compares masses and gives the same reading anywhere.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.g in terms of G, M, R?Show answer
g = GM/R².
2.1 kgf in N?Show answer
9.8 N.
3.1 gf in dyne?Show answer
980 dyne.
4.Instrument for weight?Show answer
Spring balance.
5.Does g depend on the falling body’s mass?Show answer
No.

Mass, Weight and Acceleration Due to Gravity (g): frequently asked questions

What is the difference between mass and weight?

Mass is the amount of matter in a body (scalar, kg, constant everywhere); weight is the force of gravity on it (vector, newton, W = mg, changes with g).

What is the acceleration due to gravity?

The acceleration produced in a freely falling body by the planet’s pull; on the Earth’s surface it is about 9.8 m s⁻², equal to GM/R².

Why do a heavy and a light body fall together in a vacuum?

Both have the same acceleration g = GM/R², because the body’s mass cancels out in mg = GMm/R².