NEET Physics — Newton's Laws of Motion

Linear Momentum – Complete Notes, Revision, Important Questions & Downloads

Linear momentum (p = mv) is the product of mass and velocity of a body. It is a vector quantity in the direction of velocity, measured in kg·m/s and with dimensions [M L T⁻¹]. NEET tests momentum through direct calculations (finding p), comparing momenta of bodies with equal kinetic energy or equal mass, and understanding the vector nature of momentum. The key NEET concept: two bodies with equal momentum have different speeds if their masses differ — the lighter body has greater speed.

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3 SubtopicsNewton's Laws Ch.4p = mv

Expected QuestionsQ

0–1

Linear momentum as a standalone topic appears occasionally in NEET. More often it appears as part of conservation of momentum problems or impulse-momentum questions. Expect 1 direct question every 2 years on this topic alone.

Time Required⏱

45 min

15 min for definition, formula, vectors and units; 15 min for comparison problems (equal momentum / equal KE); 15 min for MCQ practice.

Difficulty⚡

Easy–Medium

The formula is simple (p = mv). Difficulty arises in comparison problems where students must compare p and KE for bodies with different masses — requiring algebraic manipulation of p = mv and KE = p²/2m.

NRI USA Curriculum GapUS

Low

AP Physics 1 and AP Physics C both cover linear momentum thoroughly. The NEET-specific emphasis is on the relationship between KE and momentum (KE = p²/2m) and comparison problems which are common in NEET but less so in AP exams.

3Subtopics

8+Practice Questions

4Free Downloads

45 minPrep Time

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NEET Weightage — Linear Momentum

Newton's Laws of Motion (Chapter 4)

NEET Year	Questions from this Topic	Bar	Marks
2024	1	1 Q	4
2023	0	0 Q	0
2022	1	1 Q	4
2021	0	0 Q	0
2020	1	1 Q	4
2019	0	0 Q	0
6-Year Total (2019–2024)	2–4		8–16

p = mv. Units: kg·m/s. Dimensions: [M L T⁻¹]. Vector in direction of velocity. NEET tests units and dimensions in assertion-reason questions.
Key comparison: If two bodies have equal momentum (p₁=p₂ → m₁v₁=m₂v₂), lighter body has greater velocity. KE = p²/2m → for equal p, lighter body has greater KE.
Rate of change of momentum = Applied force (Newton's Second Law form): F = dp/dt = d(mv)/dt. This form of Second Law is more general than F = ma and is sometimes tested in NEET.

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0.7

Avg Questions / Year

🎯

Total Marks (6 yrs)

📈

Direct

Pattern

⚠️

Easy–Medium

Difficulty

How to Prepare Linear Momentum for NEET

Master p = mv and the KE–momentum bridge Momentum p = mv. Kinetic energy KE = ½mv² = p²/2m. From KE=p²/2m: (1) for equal mass — higher KE means higher p; (2) for equal p — lighter body has higher KE; (3) for equal KE — lighter body has lower p. These three relations generate a class of NEET comparison questions.

Vector direction is the same as velocity Momentum is a vector. Its direction is identical to the direction of velocity. When velocity reverses (e.g., ball bouncing), momentum direction reverses too. Change in momentum = final p⃗ − initial p⃗ (requires vector subtraction, not just magnitude difference).

Know the special case: F = dp/dt Newton's Second Law in its most general form is F = dp/dt. For constant mass, dp/dt = m × dv/dt = ma. NEET occasionally tests the F = dp/dt form directly in questions about variable mass systems or impulse (impulse = Δp = F × Δt).

Memorise the units and dimensions exactly p = mv: units kg·m/s = N·s (newton-second). Dimensions: [M][L T⁻¹] = [M L T⁻¹]. The N·s form is tested in unit conversion and dimensional analysis questions.

Study Materials — Linear Momentum

PDF · Cheat Sheet · MCQ Set · PYQ

📘

Full Notes

Definition, formula, units, and dimensions of linear momentum. Vector nature. Comparisons at equal momentum, equal KE, equal velocity. Relation to Newton's Second Law (F = dp/dt).

3 subtopics4 pagesFormula-rich

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Formula Sheet

p = mv; KE = p²/2m; dimensions [M L T⁻¹]; unit = kg·m/s = N·s; F = dp/dt; impulse J = Δp = F·Δt; comparison table (equal p/mass/KE scenarios).

6 formulas1 pageComparison table

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MCQ Practice

15 questions: calculating p, comparing p and KE for bodies with different masses, dimensional analysis, vector nature of momentum change (direction reversal), and impulse = change in momentum.

15 MCQsWith solutionsRanked by frequency

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PYQ

Year-tagged NEET questions on linear momentum — p = mv calculations, KE–p comparison, impulse-momentum, direction of momentum change (vectors), and Newton's second law as F = dp/dt.

10+ year-tagged Qs2015–2024Step-by-step solutions

Download PYQs

Subtopics in Linear Momentum

2-Column Table

Column A	Column B
Object with zero dimension↗	Point mass↗
Linear momentum of a body↗

Rapid Revision — Linear Momentum

Concept → Trap → Example

1) Definition and Formula

Core

Linear momentum of a body is the product of its mass and velocity: p = mv. It measures the quantity of motion — how hard it is to stop a body. More massive bodies or faster bodies are harder to stop.

p = mv. For a 0.5 kg ball moving at 20 m/s: p = 0.5 × 20 = 10 kg·m/s.
At rest, v = 0 → p = 0. No momentum when at rest, regardless of mass.
NEET: 'If the speed of a body doubles while mass is constant, its momentum' → also doubles (linear relationship). KE quadruples (p²/2m → (2p)²/2m = 4 × original KE).

Example (NEET-style)A truck of mass 5000 kg moving at 2 m/s and a car of mass 1000 kg moving at 10 m/s — which has more momentum? Truck: p = 5000 × 2 = 10,000 kg·m/s. Car: p = 1000 × 10 = 10,000 kg·m/s. Equal momentum! But their speeds are very different — demonstrating equal momentum with different masses.

2) Vector Nature and Units

Core

Momentum is a vector quantity with direction identical to velocity. Units: kg·m/s = N·s. Dimensions: [M L T⁻¹]. When a body changes direction, its momentum changes even if speed is constant (since direction of p changes with direction of v).

Change in momentum: Δp⃗ = p⃗f − p⃗i. For a ball bouncing off a wall at the same speed: |Δp| = 2mv (directions opposite, so magnitude of change = 2mv).
Impulse J = Δp⃗ = F⃗ × Δt. Units of impulse = units of momentum = N·s.
NEET: 'SI unit of linear momentum' → kg·m/s. 'Dimension of momentum' → [M L T⁻¹]. Both are direct NEET questions.

Example (NEET-style)A 0.2 kg ball hits a wall at 15 m/s perpendicular to the wall and bounces back at 15 m/s. Change in velocity = 15−(−15) = 30 m/s (opposite directions). Change in momentum = 0.2 × 30 = 6 kg·m/s. The wall exerts an impulse of 6 N·s on the ball.

3) Comparison at Equal Momentum

NEET-Key

When two bodies have equal momentum (m₁v₁ = m₂v₂), the lighter body moves faster. When comparing KE for equal momentum: KE = p²/2m → smaller m gives larger KE. So with equal momentum, the lighter body has more kinetic energy.

Equal momentum, different mass: m₁v₁ = m₂v₂ → v₁/v₂ = m₂/m₁ (heavier body slower).
Equal momentum, compare KE: KE₁/KE₂ = m₂/m₁ (for equal p: KE = p²/2m). Lighter body has higher KE.
Equal KE, compare momentum: p = √(2m × KE). For equal KE: p₁/p₂ = √(m₁/m₂). Heavier body has more momentum at equal KE.

Example (NEET-style)Two bodies A (mass 2 kg) and B (mass 8 kg) have the same linear momentum p. Find ratio of their KEs. KE_A = p²/(2×2) = p²/4. KE_B = p²/(2×8) = p²/16. KE_A/KE_B = (p²/4)/(p²/16) = 4. A has 4× more KE than B for same p. A is lighter, so has higher KE.

US Curriculum Gaps — Linear Momentum

Topics in this section are tested in NEET but organised differently in standard US physics courses.

KE–Momentum Comparison Problems (AP Physics 1 Gap)

AP Physics 1 covers both KE and momentum but rarely asks direct comparison problems of the form: 'Two bodies have equal momentum; which has higher KE?' These questions are a NEET staple. The key is KE = p²/2m — for equal momentum, lighter body has higher KE. US students must practice this comparison explicitly for NEET.

AP Physics 1 focuses on conservation laws separately (energy conservation; momentum conservation) not cross-comparisons
NEET uses p = mv and KE = p²/2m in tandem — must derive the ratio KE₁/KE₂ = m₂/m₁ (for equal p) or p₁/p₂ = √(m₁/m₂) (for equal KE)
This is tested every 2–3 years in NEET directly as a numerical or multiple-choice comparison

Newton's Second Law as F = dp/dt (AP Physics C: Mechanics Gap)

AP Physics 1 presents F = ma primarily. AP Physics C covers F = dp/dt for variable mass. NEET expects students to know both forms and apply F = dp/dt as the more general statement. The NEET textbook introduces F = dp/dt in the momentum section before deriving F = ma as a special case.

NEET: 'Rate of change of momentum is equal to applied net force' — this is F = dp/dt (Newton's Second Law, general form)
For constant mass: F = dp/dt = d(mv)/dt = m(dv/dt) = ma → reduces to familiar form
Variable mass problems (rocket, sand pouring) require F = dp/dt and appear in NEET as reasoning questions

NEET-Style Practice Questions — Linear Momentum

4 Questions

1A body of mass 4 kg moving at 6 m/s has the same linear momentum as a body of mass 2 kg. What is the speed of the second body?p = mv

6 m/s

12 m/s

3 m/s

8 m/s

p₁ = m₁v₁ = 4 × 6 = 24 kg·m/s. For equal momentum p₂ = 24 kg·m/s = m₂v₂ = 2 × v₂. So v₂ = 24/2 = 12 m/s. The lighter body moves at twice the speed — consistent with m₁v₁ = m₂v₂ → v₂ = (m₁/m₂)v₁ = (4/2) × 6 = 12 m/s.

2Two bodies A (mass m) and B (mass 4m) have the same linear momentum. The ratio of their kinetic energies KE_A : KE_B is:KE-Momentum

1 : 4

4 : 1

1 : 2

2 : 1

For equal momentum p, KE = p²/2m. KE_A = p²/2m; KE_B = p²/2(4m) = p²/8m. KE_A/KE_B = (p²/2m)/(p²/8m) = 8m/2m = 4. So KE_A : KE_B = 4 : 1. The lighter body (A, mass m) has 4 times the kinetic energy of the heavier body (B, mass 4m) for the same momentum.

3The dimension of linear momentum is:Dimensions

[M L T⁻²]

[M L T⁻¹]

[M L² T⁻²]

[M L² T⁻¹]

p = mv. Dimension of mass = [M]. Dimension of velocity = [L T⁻¹]. So dimension of momentum = [M][L T⁻¹] = [M L T⁻¹]. Note: [M L T⁻²] is force (F=ma), [M L² T⁻²] is energy, [M L² T⁻¹] is angular momentum — common distractors.

4A 0.5 kg ball moving at 10 m/s east bounces off a wall and moves at 8 m/s west. The magnitude of change in its momentum is:Vector Momentum

1 kg·m/s

9 kg·m/s

5 kg·m/s

4 kg·m/s

Taking east as positive: initial p = +0.5×10 = +5 kg·m/s; final p = −0.5×8 = −4 kg·m/s (west = negative). Δp = final − initial = −4 − (+5) = −9 kg·m/s. Magnitude |Δp| = 9 kg·m/s. Note: the ball lost speed (10→8) but the direction reversal means the change in momentum is large (9 kg·m/s), not small.

Practice Problems — Linear Momentum

Click "Reveal Answer" after attempting

1A bullet of mass 10 g moving at 400 m/s embeds in a wooden block of mass 990 g at rest. Find the momentum of the system after embedding.

4 kg·m/s

0.4 kg·m/s

40 kg·m/s

400 kg·m/s

👁 Reveal Answer

Answer: 4 kg·m/s. Initial momentum of bullet = mv = 0.010 × 400 = 4 kg·m/s. Block was at rest so p = 0. Total initial momentum = 4 kg·m/s. By conservation of momentum, total final momentum = 4 kg·m/s (momentary impact doesn't change this).

2Body A has mass 1 kg and speed 10 m/s. Body B has mass 4 kg and speed 5 m/s. Which has greater momentum? Which has greater KE?

A has more p; B has more KE

B has more p; A has more KE

A has more p and KE

B has more p and KE

👁 Reveal Answer

B has greater momentum; A has greater KE. p_A = 1×10 = 10 kg·m/s; p_B = 4×5 = 20 kg·m/s → B has more p. KE_A = ½(1)(10²) = 50 J; KE_B = ½(4)(5²) = 50 J → Equal KE! Both have the same kinetic energy. (This is a trap — different speeds, different masses, but equal KE.)

3If the kinetic energy of a body is doubled (mass unchanged), by what factor does its momentum increase?

√2 times

2 times

4 times

√2/2 times

👁 Reveal Answer

√2 times. KE = p²/2m → p = √(2m·KE). If KE → 2KE: p_new = √(2m·2KE) = √2 × √(2m·KE) = √2 × p_original. So momentum increases by factor √2.

4Two bodies of equal mass m moving with equal speeds v in opposite directions collide head-on and stick together. Find the final momentum.

2mv

mv/2

👁 Reveal Answer

0. Equal masses, equal speeds, opposite directions: p₁ = +mv (right), p₂ = −mv (left). Total momentum = +mv + (−mv) = 0. After sticking together: total momentum = 0 (conservation of momentum). The combination is at rest.

Physics — Newton's Laws of Motion Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

Definition and Formula: Write p = mv. State: 'Linear momentum is the quantity of motion of a body.' Compute p for a 2 kg body at 5 m/s: p = 10 kg·m/s. State that p = 0 when body is at rest. Confirm units: kg·m/s = N·s.

Vector Nature and Units: State that momentum is a vector in the direction of velocity. Write dimensions [M L T⁻¹]. Compute Δp⃗ = p⃗f − p⃗i for a body reversing direction: use signed values. Practice: ball bouncing → |Δp| = 2mv if speeds same, sign reversal.

Comparison at Equal Momentum: Derive KE = p²/2m. For equal p: KE ∝ 1/m → lighter body has more KE. For equal KE: p ∝ √m → heavier body has more p. Confirm with a worked example: two bodies, same p, find ratio KE_1:KE_2.

F = dp/dt: State Newton's Second Law in momentum form: F = dp/dt. For constant mass → F = ma. For variable mass (rocket): F = v(dm/dt). Write the impulse-momentum theorem: J = F·Δt = Δp. State units of impulse = N·s = kg·m/s.

NEET Comparison Table: Write the cross-comparison table: (1) Same mass, double speed → p doubles, KE quadruples; (2) Same p, mass doubles → KE halves, speed halves; (3) Same KE, mass doubles → p increases by √2. Solve one numerical for each case.

FAQ — Linear Momentum

Notes · Downloads · Revision · Important Questions

What is linear momentum?

Linear momentum of a body is the quantity of motion contained in the body. It is defined as the product of mass and velocity: p = mv. It is a vector quantity — direction is the same as the direction of velocity.

What are the units and dimensions of linear momentum?

Units: kg·m/s (SI). This is also equivalent to N·s (newton-second). Dimensions: [M L T⁻¹]. Derived: p = mv → [M][L T⁻¹] = [M L T⁻¹]. Common distractor in NEET: [M L T⁻²] is force, not momentum.

Is momentum a scalar or vector?

Momentum is a vector quantity. Its direction is identical to the direction of velocity. When velocity changes direction (as in a bouncing ball), the momentum direction changes too. The magnitude of change in momentum requires vector subtraction, not just |p₂| − |p₁|.

Two bodies have the same momentum. How do their speeds compare?

If m₁v₁ = m₂v₂ (same p), then v₁/v₂ = m₂/m₁. The lighter body moves faster: if m₁ < m₂, then v₁ > v₂. Example: a 2 kg body and a 10 kg body have the same momentum. The 2 kg body moves at 5× the speed of the 10 kg body.

If two bodies have the same momentum, which has greater kinetic energy?

The lighter body. KE = p²/2m. For equal p, KE is larger when m is smaller. Example: two bodies (mass m and 4m) have same p. KE₁ = p²/2m; KE₂ = p²/8m. KE₁/KE₂ = 4. The lighter body (mass m) has 4× more kinetic energy.

How is Newton's Second Law related to momentum?

Newton's Second Law in its most general form: F = dp/dt (rate of change of momentum = applied net force). For constant mass: F = d(mv)/dt = m(dv/dt) = ma. This is the F = ma form. The more general form F = dp/dt applies even when mass changes (e.g., rocket losing fuel mass).

What is the relationship between impulse and momentum?

Impulse J = F × Δt (for constant force). By Newton's Second Law: F = Δp/Δt → F × Δt = Δp. So impulse = change in momentum. Units: J (impulse) = N·s = kg·m/s (same as momentum). A large force for short time OR small force for long time can produce the same impulse and same change in momentum.

Does momentum of a body change if it moves at constant speed in a circle?

Yes. In uniform circular motion, speed is constant but direction continuously changes. Since momentum is a vector (p = mv⃗), changing direction means changing momentum even at constant speed. The centripetal force is what continuously changes the direction of momentum vector, so there is always a non-zero rate of change of momentum (centripetal force = Δp/Δt).

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Linear Momentum

Linear Momentum – Complete Notes, Revision, Important Questions & Downloads

1) Definition and Formula

2) Vector Nature and Units

3) Comparison at Equal Momentum

KE–Momentum Comparison Problems (AP Physics 1 Gap)

Newton's Second Law as F = dp/dt (AP Physics C: Mechanics Gap)

Physics — Newton's Laws of Motion Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Object with zero dimension

Point mass

Linear momentum of a body

Subtopics

Object with zero dimension

Point mass

Linear momentum of a body

NEET > Physics > Laws of Motion Chapters

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Linear Momentum

Overview content

Linear Momentum – Complete Notes, Revision, Important Questions & Downloads

1) Definition and Formula

2) Vector Nature and Units

3) Comparison at Equal Momentum

KE–Momentum Comparison Problems (AP Physics 1 Gap)

Newton's Second Law as F = dp/dt (AP Physics C: Mechanics Gap)

Physics — Newton's Laws of Motion Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Object with zero dimension

Point mass

Linear momentum of a body

Subtopics

Object with zero dimension

Point mass

Linear momentum of a body

NEET > Physics > Laws of Motion Chapters

Comments

Leave a comment

Comments (0)