CBSE Class 9 Science — Gravitation

Chapter Overview & Weightage

Gravitation is one of the most important chapters in CBSE Class 9 Science. It carries 5-8 marks in the annual examination — typically a 3-mark numerical (free fall, gravity, pressure) and a 2-mark conceptual question. NCERT Chapter 10 covers Universal Law of Gravitation, free fall, mass and weight, and thrust and pressure.

CBSE Class 9 Science boards: Gravitation regularly appears as a 5-mark question that combines a definition/law (2 marks) + a numerical (3 marks). The most common numerical: “Calculate weight/mass on Moon” or “Time for free fall from height h.” Prepare these specifically.

Section	Typical Marks
Universal Law of Gravitation (statement + formula)	2
Free fall numericals	3
Mass vs Weight differences	2
Thrust and Pressure	2-3

Key Concepts You Must Know

Universal Law of Gravitation (Newton, 1687): Every object in the universe attracts every other object with a force that is:

Directly proportional to the product of their masses
Inversely proportional to the square of the distance between them

Free fall: When an object falls only under gravity (no air resistance), it’s called free fall. The acceleration due to gravity $g = 9.8$ m/s² acts downward.

Mass vs Weight:

Mass = amount of matter in an object (measured in kg, constant everywhere)
Weight = gravitational force on the object = $mg$ (measured in N, varies with $g$ )

g on Moon = g/6: The value of $g$ on the Moon is $1.63$ m/s², approximately one-sixth of Earth’s $g$ . So weight on Moon = (1/6) × weight on Earth.

Thrust: Force acting perpendicular to a surface.

Pressure: Thrust per unit area.

Important Formulas

F = G\frac{m_1 m_2}{r^2}

where:

$G = 6.674 \times 10^{-11}$ N·m²/kg² (Universal Gravitational Constant)
$m_1, m_2$ = masses of the two objects
$r$ = distance between their centres

On Earth’s surface:

g = \frac{GM}{R^2} = 9.8 \text{ m/s}^2

where $M$ = mass of Earth = $6 \times 10^{24}$ kg, $R$ = radius of Earth = $6.4 \times 10^6$ m.

With $u$ = initial velocity, taking downward as positive:

v = u + gt

s = ut + \frac{1}{2}gt^2

v^2 = u^2 + 2gs

For an object dropped from rest: $u = 0$ .

W = mg \quad \text{(Weight in Newtons)}

P = \frac{F}{A} = \frac{\text{Thrust}}{\text{Area}} \quad \text{(Pressure in Pa)}

Solved Previous Year Questions

PYQ 1 — Free Fall Numerical

Q: An object is dropped from a height of 20 m. How long will it take to reach the ground? (g = 10 m/s²)

Solution:

$u = 0$ , $s = 20$ m, $g = 10$ m/s², $t = ?$

Using $s = ut + \frac{1}{2}gt^2$ :

20 = 0 + \frac{1}{2} \times 10 \times t^2

t^2 = \frac{20}{5} = 4 \Rightarrow t = 2 \text{ s}

PYQ 2 — Weight on Moon

Q: A man weighs 600 N on Earth. What is his weight on the Moon?

Solution:

$g_{\text{Moon}} = g_{\text{Earth}} / 6$

W_{\text{Moon}} = \frac{W_{\text{Earth}}}{6} = \frac{600}{6} = 100 \text{ N}

His mass remains the same everywhere: $m = W/g = 600/10 = 60$ kg. Only weight changes.

PYQ 3 — Universal Law Application

Q: The gravitational force between two objects is $F$ . What will the force become if: (a) the distance is doubled? (b) the mass of one object is tripled?

Solution:

(a) $F \propto 1/r^2$ . If $r \to 2r$ : $F' = F/4$ . Force becomes one-fourth.

(b) $F \propto m_1$ . If $m_1 \to 3m_1$ : $F' = 3F$ . Force triples.

PYQ 4 — Pressure

Q: A wooden block of weight 500 N has dimensions 2 m × 0.5 m × 0.1 m. Find the maximum and minimum pressure it can exert.

Solution:

The pressure exerted = Weight/Area.

Minimum pressure (maximum area face = 2 m × 0.5 m = 1 m²): $P_{min} = 500/1 = 500$ Pa

Maximum pressure (minimum area face = 0.5 m × 0.1 m = 0.05 m²): $P_{max} = 500/0.05 = 10{,}000$ Pa

Difficulty Distribution

Difficulty	Question Type	Example
Easy (40%)	State laws, define terms, simple comparisons	State Newton’s law, difference between mass and weight
Medium (40%)	3-mark numericals	Free fall time, weight on Moon, force change
Hard (20%)	Derivations, multi-step problems	Derive $g = GM/R^2$ , projectile on Moon

Expert Strategy

Memorise $G$ and $g$ carefully. $G = 6.674 \times 10^{-11}$ N·m²/kg² (Universal Gravitational Constant — same everywhere in the universe). $g = 9.8$ m/s² (acceleration on Earth’s surface — different on Moon, Mars, etc.). CBSE questions explicitly use $g = 10$ m/s² in calculations unless specified, to make arithmetic easier.

The 5 equations of motion are the same for free fall — just substitute $a = g$ . If thrown upward, $g$ is negative (taking upward as positive). If dropped or thrown downward, $g$ is positive. Consistent sign convention throughout a problem is essential.

For the Universal Law question, always write: (1) the statement in words, (2) the mathematical formula, (3) define each symbol, (4) units of $G$ . That’s 4 sub-parts and CBSE gives 1 mark each.

For derivation of $g = GM/R^2$ : Use Newton’s second law: $F = mg$ , and the Universal Law: $F = GMm/R^2$ . Equate: $mg = GMm/R^2 \Rightarrow g = GM/R^2$ . Simple and full marks.

Common Traps

Trap 1: Writing “Weight is measured in kg.” No — weight is a force, measured in Newtons (N). Mass is measured in kg. This confusion costs 1 mark frequently. Remember: weighing scales typically show mass (kg), not weight (N) — they’re calibrated to display mass.

Trap 2: Using $g = 9.8$ m/s² when CBSE paper says “take $g = 10$ m/s²” in the problem. Always read the given values carefully. Using 9.8 when 10 is specified will give a wrong numerical answer.

Trap 3: In “force doubles if distance halves” type questions: $F \propto 1/r^2$ . If $r$ becomes $r/2$ : $F' \propto 1/(r/2)^2 = 4/r^2 = 4F$ . Force becomes 4 times, not 2 times. The inverse square law is sometimes confused with an inverse (not inverse square) relationship.

Trap 4: Applying free fall equations to objects thrown horizontally (like a ball thrown off a cliff). The horizontal component has no acceleration; only the vertical component uses $g$ . Class 9 sticks to purely vertical free fall, but be careful not to over-apply.