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.

Formula sheet (PDF) →

Physics · Chapter 1

Laws of Motion

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

7 formulas · 3 solved examples · 5 practice questions · Board weight: 5 marks · Maharashtra State Board Class 10

Not in the 2025–26 syllabus. This chapter is not part of the Maharashtra SSC (Std X) syllabus for 2025–26. It is kept here for reference.

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 favourite

F = ma

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

Linear MomentumBoard favourite

p = m v

Impulse

J = F Δ t = Δ p = m (v - u)

Conservation of Linear MomentumBoard favourite

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.