Is it correct to say: Confusing mass and weight?

Mass is scalar (kg); weight is force (N). Weight changes with g, mass does not.

Is it correct to say: Treating action and reaction as acting on same body?

Newton's third law forces act on two different bodies — they never cancel each other.

Is it correct to say: Forgetting to convert grams to kilograms?

SI unit of mass is kg. 20 g = 0.02 kg. Missing this factor of 1000 changes answer drastically.

Is it correct to say: Using F = ma without net force?

F must be the resultant of all forces on the body. Sum vectors first.

Is it correct to say: Applying conservation of momentum when external forces are present?

Conservation holds only for isolated systems (no net external force).

Is it correct to say: Writing impulse in N instead of N·s?

Impulse has units of N·s or kg·m/s — same as momentum.

Laws of Motion

Newton's three laws, momentum, impulse and applications — Maharashtra Board Class 10 Physics

📐 7 formulas✏️ 3 examples🎯 5 practice⚖️ 5 marks🏫 Maharashtra State Board📚 Class 10✓ 2025–26 syllabus

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Board Exam Tips

→State + explain Newton's three laws with everyday examples — 3-mark repeat question.
→Derivation of F = ma from second law is a definite 2-mark ask.
→Numericals on conservation of momentum (recoil, collisions) carry 3 marks.
→Impulse = F·t = change in momentum — remember both forms.
→Draw a free-body diagram before solving any force problem — helps avoid sign mistakes.

📊 Diagram

Free-body diagram: applied force, weight and normal on a block

📐 Formulas(7)

Newton's Second Law (Force)★ Board fav

F = ma

Symbol	Meaning
$F$	Net force (N)
$m$	Mass of the body (kg)
$a$	Acceleration (m/s²)

Linear Momentum★ Board fav

p = m v

Impulse

J = F Δ t = Δ p = m (v - u)

Conservation of Linear Momentum★ Board fav

m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}

Weight (Special Case of F = ma)

W = m g

Recoil Velocity (from Momentum Conservation)

V = - \frac{m v}{M}

Apparent Weight in Lift

R = m (g \pm a)

✏️ Solved Examples

1Solved Exampleeasy3 steps

A force of 20 N is applied on a body of mass 4 kg initially at rest. Find (i) acceleration and (ii) velocity after 5 s.

Apply Newton's second law

a = \frac{F}{m} = \frac{20}{4} = 5 m/s^{2}

2Solved Exampleboard4 steps

A bullet of mass 20 g is fired horizontally with a velocity of 400 m/s from a gun of mass 5 kg. Calculate the recoil velocity of the gun.

Convert masses to kg and note initial momentum is zero

m = 0.02 kg, M = 5 kg, u = 0

3Solved ExampleHOTS5 steps

A 60 kg man stands in a lift. Find his apparent weight when the lift (a) moves up with acceleration 2 m/s², (b) moves down with acceleration 2 m/s², (c) is in free fall. (g = 10 m/s²)

General formula R = m(g ± a)

R = m (g \pm a)

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Confusing mass and weight
✓Mass is scalar (kg); weight is force (N). Weight changes with g, mass does not.
2
Treating action and reaction as acting on same body
✓Newton's third law forces act on two different bodies — they never cancel each other.
3
Forgetting to convert grams to kilograms
✓SI unit of mass is kg. 20 g = 0.02 kg. Missing this factor of 1000 changes answer drastically.
4
Using F = ma without net force
✓F must be the resultant of all forces on the body. Sum vectors first.
5
Applying conservation of momentum when external forces are present
✓Conservation holds only for isolated systems (no net external force).
6
Writing impulse in N instead of N·s
✓Impulse has units of N·s or kg·m/s — same as momentum.

🎯 Practice Yourself

🎯Practice Yourself5 questions

Q1
State Newton's first law of motion and give one example.
Q2
A force of 5 N acts on a body of mass 2 kg for 4 s. Find the change in momentum.
Q3
A body of mass 10 kg moves with velocity 5 m/s and collides with another body of mass 5 kg at rest. If they move together after collision, find their common velocity.
Q4
State the SI unit and definition of one newton.
Q5
A cricket player 'draws back' his hands while catching a fast ball. Explain.

📝 Notes

Newton's Laws of Motion — Maharashtra SSC

The Maharashtra Board keeps Newton's laws in Class 10 (unlike CBSE, which places them in Class 9). Expect a mix of statement questions, derivations and short numericals.

The three laws in one line each

First law (Inertia): a body preserves its state of rest or uniform motion unless a net external force acts.
Second law: F = ma — force is directly proportional to rate of change of momentum.
Third law: every action has an equal and opposite reaction — the two forces act on different bodies.

Momentum — the heart of the second law

Newton actually wrote the second law as F = dp/dt. For constant mass this reduces to F = ma. But when mass changes (rockets), you must use the momentum form.

Everyday illustrations for board answers

First law: dust flying off a shaken carpet; passengers jerked forward when a bus stops suddenly.
Second law: heavier body needs more force to gain the same acceleration.
Third law: rocket propulsion, walking, swimming, gun recoil.

Free-body diagram routine

Isolate the body.
Mark every force acting on it (weight, normal, friction, applied, tension).
Choose axes (x horizontal, y vertical).
Apply ΣF = ma along each axis.

Board vs CBSE

Maharashtra SSC often gives combined problems — Newton's laws with kinematics (find a, then use v = u + at). CBSE Class 9 tends to separate them. Practise SSC-style multi-step numericals.