Gravitation ICSE Class 9: Universal Law, Acceleration due to Gravity, Mass and Weight

What Gravitation is about

Weightage: CISCE publishes no chapter weightage and no question-paper layout for ICSE Class 9 Physics. Class IX is examined by your school: one 80-mark paper of 2 hours plus 20 marks of internal assessment. Gravitation is in the 3. Laws of Motion (v) part of the 2028 syllabus.Source: CISCE ICSE 2028 Physics syllabus, Class IX

Key concepts

Universal law of gravitation

Statement: every body in the universe attracts every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

$F=G\frac{m_1{m}_2}{r^2}$

Here $G$ is the universal gravitational constant: $G=6.67\times 10^{-11}$ N m² kg⁻². It has the same value everywhere in the universe. The force acts along the line joining the centres, is always attractive, and the two bodies pull each other with equal and opposite forces (third law).

Worked example

Find the gravitational force between two 100 kg spheres whose centres are 1 m apart.

Try it first, then show the solutionSolution

1. $F=\frac{6.67\times 10^{-11}\times 100\times 100}{1^2}$.
2. $F=6.67\times 10^{-7}$ N.

Answer: 6.67 × 10⁻⁷ N (very small)

Ratio questions on the law

Because $F\propto \frac{m_1{m}_2}{r^2}$, you can find a new force without knowing $G$:

• double one mass → $F$ doubles; double both → $4F$;
• double the distance → $\frac{F}{4}$; halve it → $4F$;
• triple the distance → $\frac{F}{9}$.

Write $\frac{F_2}{F_1}=\frac{m_1^{\prime }{m}_2^{\prime }}{m_1{m}_2}\times {\left(\frac{r_1}{r_2}\right)}^2$.

Worked example

The force between two bodies is 36 N. Find the force if one mass is doubled and the distance is tripled.

Try it first, then show the solutionSolution

1. $\frac{F_2}{F_1}=2\times {\left(\frac{1}{3}\right)}^2=\frac{2}{9}$.
2. $F_2=36\times \frac{2}{9}=8$ N.

Answer: 8 N

Importance and applications of the law

The law of gravitation explains:

• why bodies fall to the Earth and why we have weight;
• the motion of the Moon round the Earth and of the planets round the Sun (gravity provides the pull towards the centre);
• tides in the sea, caused mainly by the Moon's pull;
• why the Earth holds its atmosphere;
• the motion of artificial satellites.

The force between everyday objects is tiny (as in the 100 kg example), so we notice gravity only when at least one body is as massive as the Earth.

Worked example

If the Earth attracts an apple with a force, the apple attracts the Earth with an equal force. Why does the apple fall towards the Earth and not the Earth towards the apple?

Try it first, then show the solutionSolution

1. The forces are equal (third law).
2. Acceleration $=\frac{F}{m}$; the Earth's mass ($6\times 10^{24}$ kg) is enormous, so its acceleration is far too small to notice.
3. The apple's small mass gives it a large acceleration (9.8 m s⁻²).

Answer: Equal forces, but the Earth's huge mass makes its acceleration negligible.

Gravity, g and free fall

Gravity is the force with which the Earth pulls a body towards its centre. The acceleration it produces is the acceleration due to gravity, $g$, about $9.8$ m s⁻² near the Earth's surface, the same for all bodies at a place.

Using the law: for a mass $m$ on the surface of the Earth (mass $M$, radius $R$), $mg=\frac{GMm}{R^2}$, so $g=\frac{GM}{R^2}$. It does not depend on the mass of the falling body.

Free fall: motion under gravity alone (no air resistance). A feather and a coin fall together in a vacuum. Use the equations of motion with $a=g$.

Worked example

Using $G=6.67\times 10^{-11}$ N m² kg⁻², $M=6\times 10^{24}$ kg and $R=6.4\times 10^6$ m, find $g$ at the Earth's surface.

Try it first, then show the solutionSolution

1. $g=\frac{6.67\times 10^{-11}\times 6\times 10^{24}}{(6.4\times 10^6{)}^2}$.
2. $=\frac{4.002\times 10^{14}}{4.096\times 10^{13}}$.
3. $\approx 9.77$ m s⁻².

Answer: ≈ 9.8 m s⁻²

Mass and weight

Mass is the quantity of matter in a body. Weight is the force with which the Earth (or any planet) attracts it: $W=mg$.

Compared point by point:

• mass is a scalar; weight is a force, a vector, directed towards the centre of the Earth;
• mass is constant everywhere; weight depends on $g$, so it changes from place to place (it is zero in deep space far from all bodies);
• SI unit of mass: kg; of weight: N;
• mass is measured with a beam (physical) balance; weight with a spring balance.

Worked example

Find the weight of a 50 kg girl in newtons and in kgf ($g=9.8$ m s⁻²).

Try it first, then show the solutionSolution

1. $W=mg=50\times 9.8=490$ N.
2. In gravitational units: $W=50$ kgf.

Answer: 490 N = 50 kgf

Gravitational units of force

The weight of a standard mass gives handy units of force:

• 1 kgf = weight of 1 kg $=1\times 9.8=9.8$ N.
• 1 gf = weight of 1 g $=1\times 980$ cm s⁻² $=980$ dyne.

So a body of mass $m$ kg has weight $m$ kgf, which is $9.8m$ N. To change N to kgf, divide by 9.8.

These units are convenient (a 5 kg bag weighs 5 kgf) but depend on $g$, which is why the SI unit, the newton, is preferred for calculations.

Worked example

A body weighs 196 N on the Earth. Find its weight in kgf and its mass ($g=9.8$ m s⁻²).

Try it first, then show the solutionSolution

1. $\frac{196}{9.8}=20$ kgf.
2. Mass $=\frac{W}{g}=20$ kg.

Answer: 20 kgf; 20 kg

Physics in real life: Gravitation

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.

Topics in this chapter

• Mass, Weight and Acceleration Due to Gravity (g)
• Universal Law of Gravitation: F = Gm₁m₂/r² and Ratio Problems

Gravitation formula sheet

Universal law

$F=G\frac{m_1{m}_2}{r^2}$

r between centres.

Gravitational constant

$G=6.67\times 10^{-11}{\text{N m}}^2{\text{kg}}^{-2}$

Same everywhere.

Acceleration due to gravity

$g=\frac{GM}{R^2}$

≈ 9.8 m s⁻² on Earth.

Weight

$W=mg$

N; vector, towards the centre.

Gravitational units

$1\text{kgf}=9.8\text{N};1\text{gf}=980\text{dyne}$

Weight of 1 kg / 1 g.

Ratio form

$\frac{F_2}{F_1}=\frac{m_1^{\prime }{m}_2^{\prime }}{m_1{m}_2}{\left(\frac{r_1}{r_2}\right)}^2$

No need for G.

Gravitation: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the school exam asks Gravitation

The question patterns to expect, and the method that works for each.

Tricks to remember Gravitation

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

• Masses multiply, distance divides twice

  Top: m₁ × m₂. Bottom: r × r.

  Use it when: Writing the law.

• Double the gap, quarter the pull

  Distance ×2 → force ÷4; distance ×3 → force ÷9.

  Use it when: Ratio questions.

• Mass stays, weight travels

  Mass is the same everywhere; weight changes with g.

  Use it when: Mass vs weight.

• kgf = kg on the label

  A 7 kg bag weighs 7 kgf = 7 × 9.8 N.

  Use it when: Gravitational units.

Gravitation: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section B style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 9-mark question split into 2 + 3 + 4 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Gravitation

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

• ✗Mistake: Forgetting to square the distance

  $F\propto \frac{1}{r^2}$; students divide by $r$ only.

  Wrong working

  Distance doubled → $\frac{F}{2}$

  Right working

  Distance doubled → $\frac{F}{4}$

  ✓Do this: Write $(r_1/r_2{)}^2$ explicitly.

  Usually costs: 1 mark.

• ✗Mistake: Mixing up G and g

  $G$ is a universal constant ($6.67\times 10^{-11}$ N m² kg⁻²); $g$ is an acceleration that depends on the planet (≈ 9.8 m s⁻² on Earth).

  ✓Do this: Write both symbols with their units.

  Usually costs: 1 mark.

• ✗Mistake: Giving weight in kg

  kg is a unit of mass. Weight is a force: N or kgf.

  ✓Do this: Weight answers end in N or kgf.

  Usually costs: 1 mark.

• ✗Mistake: Thinking heavier bodies fall faster

  In free fall all bodies have the same acceleration $g$.

  ✓Do this: Remember $g=\frac{GM}{R^2}$ has no $m$ of the falling body in it.

  Usually costs: 1 mark.

• ✗Mistake: Errors with powers of ten

  Squaring $3.84\times 10^8$ gives $10^{16}$ times 14.7, often slipped.

  ✓Do this: Square the number and the power separately: $(a\times 10^n{)}^2=a^2\times 10^{2n}$.

  Usually costs: Accuracy mark.

Practice questions on Gravitation

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

1. Q1 · 1 mark · MCQExam level

   If the distance between two bodies is tripled, the gravitational force between them becomes:
   (a) 3 times
   (b) 1/3
   (c) 9 times
   (d) 1/9

   Hint

   Inverse square.

   Answer

   (d)

2. Q2 · 1 mark · MCQExam level

   Which of these does not change when a body is taken from the Earth to the Moon?
   (a) weight
   (b) mass
   (c) the reading on a spring balance
   (d) the force of gravity on it

   Hint

   Quantity of matter.

   Answer

   (b)

3. Q3 · 2 marks · Short answerExam level

   Convert (i) 2 kgf into N (ii) 500 gf into dyne.

   Hint

   9.8 and 980.

   Answer

   (i) 19.6 N (ii) $500\times 980=4.9\times 10^5$ dyne.

4. Q4 · 1 mark · Assertion-reasonHarder exam level

   Assertion (A): A body falls towards the Earth, but the Earth hardly moves towards the body.
   Reason (R): The Earth exerts a much larger force on the body than the body exerts on the Earth.
   (a) (A) is true and (R) is false.
   (b) (A) is false and (R) is true.
   (c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
   (d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).

   Hint

   Third law.

   Answer

   (a): the forces are equal; the Earth's huge mass explains (A).

5. Q5 · 2 marks · Short answerHarder exam level

   The gravitational force between two bodies is 20 N. If the mass of one is halved and the distance between them is halved, find the new force.

   Hint

   ×½ × 4.

   Answer

   $20\times \frac{1}{2}\times 4=40$ N.

6. Q6 · 3 marks · Short answerHarder exam level

   Calculate the force of gravity between a 60 kg student and the Earth (mass $6\times 10^{24}$ kg, radius $6.4\times 10^6$ m), and compare it with $mg$ ($g=9.8$ m s⁻²).

   Hint

   F = GMm/R².

   Answer

   $F=\frac{6.67\times 10^{-11}\times 6\times 10^{24}\times 60}{4.096\times 10^{13}}\approx 586$ N; $mg=588$ N. They agree (the small difference comes from rounded data).

7. Q7 · 2 marks · Short answerExam level

   A ball is dropped from a height and takes 2 s to reach the ground. Find the height and the speed on reaching the ground ($g=9.8$ m s⁻²).

   Hint

   S = ½gt².

   Answer

   $S=19.6$ m; $v=19.6$ m s⁻¹.

8. Q8 · 2 marks · Short answerHarder exam level

   Why is a spring balance said to measure weight and a beam balance to measure mass?

   Hint

   What does each depend on?

   Answer

   A spring balance stretches according to the pull of gravity on the body (its weight), which changes with $g$. A beam balance compares the body with standard masses; both are pulled equally by gravity, so the result does not depend on $g$.

9. Q9 · 3 marks · Short answerHarder exam level

   A stone dropped from the edge of a cliff reaches the sea below in 2.5 s. Find the height of the cliff and the stone's speed just before it hits the water ($g=9.8$ m s⁻², ignore air resistance).

   Hint

   u = 0; use S = ½gt² and v = gt.

   Answer

   $S=\frac{1}{2}\times 9.8\times 6.25=30.625$ m $\approx 30.6$ m; $v=9.8\times 2.5=24.5$ m s⁻¹.

10. Q10 · 3 marks · Short answerHarder exam level

    A body weighs 49 N on the Earth. Find its mass, its weight in kgf, and the force with which it attracts the Earth.

    Hint

    Third law for the last part.

    Answer

    Mass $=5$ kg; weight $=5$ kgf; it attracts the Earth with 49 N.

11. Q11 · 4 marks · Long answerHOTS / competency

    Two identical lead spheres, each of mass 10 kg, are placed with their centres 0.2 m apart. Find the gravitational force, and explain why they do not move towards each other on a table.

    Hint

    Compare with friction.

    Answer

    $F=\frac{6.67\times 10^{-11}\times 100}{0.04}\approx 1.67\times 10^{-7}$ N. This is far smaller than the friction between the spheres and the table, so there is no unbalanced force to move them.

12. Q12 · 2 marks · Short answerHOTS / competency

    The distance between two bodies is increased by 50% and, at the same time, the mass of one of them is increased by 125%. Show that the gravitational force between them does not change.

    Hint

    Write each change as a multiplier.

    Answer

    Mass factor $=2.25$; distance factor $=1.5$, so $\frac{1}{r^2}$ factor $=\frac{1}{2.25}$. New force $=F\times 2.25\times \frac{1}{2.25}=F$: unchanged.

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. 1.Value and unit of G?Show answer

   6.67 × 10⁻¹¹ N m² kg⁻².

2. 2.Average value of g at the Earth's surface?Show answer

   About 9.8 m s⁻².

3. 3.Formula for g in terms of G?Show answer

   g = GM/R².

4. 4.1 kgf in newtons?Show answer

   9.8 N.

5. 5.Which changes from place to place: mass or weight?Show answer

   Weight.

6. 6.Which instrument measures weight?Show answer

   A spring balance.

7. 7.What happens to F if the distance is tripled?Show answer

   It becomes F/9.

8. 8.What is free fall?Show answer

   Motion of a body under gravity alone, with no air resistance.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you state the law and write the equation?
• ☐Do you square the distance in ratio questions?
• ☐Can you give the value and unit of G?
• ☐Can you derive g = GM/R² from the law?
• ☐Can you list differences between mass and weight?
• ☐Can you convert kgf to N and gf to dyne?
• ☐Can you explain tides and why the Earth does not move towards an apple?

Gravitation: frequently asked questions