Chapter 9 — Force and Laws of Motion
Welcome to HSLC Guru! This page provides complete English-medium notes, textbook question-answers, additional practice questions, glossary and formula table for Class 9 Science Chapter 9 — Force and Laws of Motion as per the ASSEB (Assam State School Education Board) syllabus. Carefully study Newton’s three laws, momentum, impulse and conservation of momentum to score full marks in your HSLC examination.
Summary
Force and Types of Forces: A force is a push or pull acting on an object that can change its state of rest or motion, change its shape, or change the direction of its motion. When two or more forces act on a body and their net effect is zero, they are called balanced forces — they do not produce acceleration but may change the shape of the object. When the net force on a body is non-zero, the forces are called unbalanced forces; only unbalanced forces can produce acceleration and change the velocity of an object. For example, when two children pull a rope with equal force in opposite directions, the rope remains stationary (balanced). If one child pulls harder, the rope moves towards that child (unbalanced).
Newton’s First Law of Motion (Law of Inertia): An object continues to be in its state of rest or of uniform motion in a straight line unless an external unbalanced force acts on it. This natural tendency of objects to resist a change in their state of rest or motion is called inertia. There are three types of inertia — inertia of rest (a body at rest tends to remain at rest, e.g., dust falls from a carpet when beaten with a stick), inertia of motion (a body in motion tends to remain in motion, e.g., a passenger falls forward when a moving bus stops suddenly), and inertia of direction (a body tends to maintain its direction of motion, e.g., mud flies off tangentially from a rotating wheel). Heavier objects have greater inertia than lighter objects, so mass is a measure of inertia.
Momentum and Newton’s Second Law: The momentum (p) of an object is the product of its mass and velocity, p = mv. Its SI unit is kg·m/s and it is a vector quantity. Newton’s Second Law states that the rate of change of momentum of an object is directly proportional to the applied unbalanced force and takes place in the direction of the force. Mathematically, F ∝ (mv − mu)/t, which gives F = ma, where ‘a’ is the acceleration. This law gives a quantitative measure of force; 1 newton (N) is the force that produces an acceleration of 1 m/s² in an object of mass 1 kg. Impulse is the product of force and the time for which it acts and equals the change in momentum: F·t = Δp = m(v − u). This explains why catching a fast-moving cricket ball with hands pulled back reduces the force on the hands by increasing the time of contact.
Newton’s Third Law and Conservation of Momentum: To every action there is an equal and opposite reaction, and they act on two different bodies. Examples include walking (we push the ground backward, the ground pushes us forward), recoil of a gun (the bullet moves forward, the gun recoils backward), and rocket propulsion (hot gases escape downward, the rocket moves upward). The Law of Conservation of Momentum states that in the absence of an external force, the total momentum of a system of objects remains constant. For two colliding bodies: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. This law is a direct consequence of Newton’s third law and applies to firing of bullets, rocket propulsion, jet engines, and collision problems.
Textbook Question Answers
Very Short Answer Questions (1 Mark)
Q1. Define force.
Answer: Force is a push or pull on an object that can change its state of rest or motion, alter its speed or direction, or change its shape and size. The SI unit of force is the newton (N).
Q2. What is inertia?
Answer: Inertia is the natural tendency of an object to resist any change in its state of rest or uniform motion in a straight line. Mass is a quantitative measure of inertia.
Q3. State the SI unit of momentum.
Answer: The SI unit of momentum is kilogram metre per second (kg·m/s). It is a vector quantity having the same direction as that of velocity.
Q4. Define 1 newton.
Answer: One newton is that force which produces an acceleration of 1 m/s² in a body of mass 1 kg. Thus, 1 N = 1 kg·m/s².
Q5. Which physical quantity is measured in kg·m/s?
Answer: Momentum is the physical quantity measured in kg·m/s.
Q6. What are balanced forces?
Answer: Two or more forces acting on an object are called balanced forces if their resultant (net) force is zero. They cannot produce acceleration but may change the shape of the body.
Q7. Give an example of inertia of motion.
Answer: When a moving bus stops suddenly, passengers jerk forward because the lower part of the body comes to rest with the bus while the upper part continues to move due to inertia of motion.
Q8. State Newton’s third law of motion.
Answer: To every action there is an equal and opposite reaction, and the action and reaction act on two different bodies simultaneously.
Q9. Why does a gun recoil when a bullet is fired?
Answer: By the law of conservation of momentum, the forward momentum of the bullet is equal in magnitude and opposite in direction to the backward momentum of the gun, causing recoil.
Q10. Name the physical quantity that is conserved during a collision in the absence of external force.
Answer: The total linear momentum of the system is conserved during a collision in the absence of an external force.
Short Answer Questions (2-3 Marks)
Q1. Distinguish between balanced and unbalanced forces.
Answer:
| Balanced Forces | Unbalanced Forces |
|---|---|
| Net resultant force is zero. | Net resultant force is non-zero. |
| Cannot produce acceleration. | Produce acceleration in the body. |
| May change the shape of the body. | Change the velocity (state of motion). |
| Example: Book lying on a table. | Example: A cricket ball hit by a bat. |
Q2. Explain the three types of inertia with one example each.
Answer: (i) Inertia of Rest: A body at rest tends to remain at rest. Example — when a carpet is beaten with a stick, dust particles fly off because the carpet moves but dust remains at rest. (ii) Inertia of Motion: A body in motion tends to continue moving. Example — passengers fall forward when a moving bus stops suddenly. (iii) Inertia of Direction: A body tends to maintain its direction of motion. Example — mud particles fly off tangentially from the wheel of a moving cycle.
Q3. Why is it advised to tie loads carefully on the roof of a bus?
Answer: When a bus accelerates, brakes suddenly or takes a sharp turn, loose luggage tends to maintain its previous state of motion (or rest) due to inertia. As a result, the load may slip off, fall forward, backward or sideways. Tying the load with ropes provides an external force that overcomes inertia and keeps the load in place, preventing accidents.
Q4. A cricket player moves his hands backward while catching a fast-moving ball. Why?
Answer: By moving his hands backward, the player increases the time (t) over which the ball’s momentum changes. Since impulse F·t = Δp is constant for a given change in momentum, increasing t decreases the force F exerted on the hands. This prevents injury to the player’s palms.
Q5. Define momentum and write its formula and SI unit.
Answer: Momentum is defined as the product of the mass and velocity of a moving body. It is denoted by p and given by the formula p = mv, where m = mass (kg) and v = velocity (m/s). Its SI unit is kg·m/s. Momentum is a vector quantity directed along the velocity. A heavy truck moving slowly may have the same momentum as a light bullet moving fast.
Q6. Why do athletes prefer to land on sand or cushions after a high jump?
Answer: Sand or a cushion increases the time of impact when the athlete lands. According to the impulse equation F = Δp/t, increasing t decreases the force exerted on the athlete’s body. Hence, landing on a soft surface reduces the chances of injury.
Long Answer Questions (5-6 Marks)
Q1. State and derive Newton’s second law of motion mathematically. Hence define 1 newton.
Answer: Statement: The rate of change of momentum of an object is directly proportional to the applied unbalanced force and takes place in the direction of the force.
Derivation: Let mass = m, initial velocity = u, final velocity = v after time t under force F.
Initial momentum = mu, Final momentum = mv.
Change in momentum = mv − mu = m(v − u).
Rate of change of momentum = m(v − u)/t.
By Newton’s second law: F ∝ m(v − u)/t.
Since (v − u)/t = a (acceleration), F ∝ ma, or F = kma.
Choosing units of F such that k = 1, we get F = ma.
Definition of 1 newton: If m = 1 kg and a = 1 m/s², then F = 1 N. Hence, one newton is that force which produces an acceleration of 1 m/s² in a body of mass 1 kg.
Q2. State and prove the law of conservation of momentum using Newton’s third law.
Answer: Statement: In the absence of an external force, the total momentum of a system of bodies remains constant.
Proof: Consider two bodies A and B of masses m₁ and m₂ moving with velocities u₁ and u₂ respectively along the same straight line (u₁ > u₂). They collide for time t, after which their velocities become v₁ and v₂.
Force exerted by A on B: F₁ = m₂(v₂ − u₂)/t.
Force exerted by B on A: F₂ = m₁(v₁ − u₁)/t.
By Newton’s third law, F₁ = −F₂.
So, m₂(v₂ − u₂)/t = −m₁(v₁ − u₁)/t.
m₂v₂ − m₂u₂ = −m₁v₁ + m₁u₁.
Rearranging: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
That is, total momentum before collision = total momentum after collision. This proves the law of conservation of momentum.
Q3. A force of 5 N gives a mass m₁ an acceleration of 10 m/s² and a mass m₂ an acceleration of 20 m/s². What acceleration would it give if both masses are tied together?
Answer: Using F = ma:
m₁ = F/a₁ = 5/10 = 0.5 kg.
m₂ = F/a₂ = 5/20 = 0.25 kg.
Combined mass = 0.5 + 0.25 = 0.75 kg.
Acceleration a = F/(m₁ + m₂) = 5/0.75 = 6.67 m/s².
Q4. A bullet of mass 20 g is fired from a gun of mass 4 kg with a velocity of 200 m/s. Calculate the recoil velocity of the gun.
Answer: Mass of bullet m₁ = 20 g = 0.02 kg; Mass of gun m₂ = 4 kg.
Initial velocities: u₁ = u₂ = 0 (both at rest).
Final velocity of bullet v₁ = 200 m/s; recoil velocity of gun = v₂.
By conservation of momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
0 = 0.02 × 200 + 4 × v₂.
v₂ = −4/4 = −1 m/s.
Negative sign indicates the gun moves in the direction opposite to the bullet. So the recoil velocity = 1 m/s.
Q5. Explain the working of a rocket on the basis of Newton’s third law and conservation of momentum.
Answer: A rocket carries fuel and an oxidiser. When the fuel burns, very hot gases are produced at high pressure and ejected backwards (downwards) through the nozzle at a great speed. According to Newton’s third law, the rocket exerts a force on the gases (action) and the gases exert an equal and opposite force on the rocket (reaction), pushing the rocket forward (upward).
From the law of conservation of momentum, the backward momentum of the ejected gases is equal in magnitude to the forward momentum gained by the rocket, since the system was initially at rest. As gases are continuously expelled, the rocket gains increasing forward velocity. This principle also applies to jet engines and squid propulsion in water.
Q6. A car of mass 1000 kg moving with a velocity of 20 m/s is brought to rest in 5 seconds by applying brakes. Calculate (i) the change in momentum, (ii) the retardation, and (iii) the force applied by the brakes.
Answer: Given: m = 1000 kg, u = 20 m/s, v = 0, t = 5 s.
(i) Change in momentum Δp = m(v − u) = 1000 × (0 − 20) = −20000 kg·m/s.
(ii) Retardation a = (v − u)/t = (0 − 20)/5 = −4 m/s².
(iii) Force F = ma = 1000 × (−4) = −4000 N.
The negative sign shows the force opposes motion (braking force = 4000 N).
Additional Practice Questions
Multiple Choice Questions (MCQ)
Q1. The SI unit of force is:
(a) kg·m/s (b) newton (c) joule (d) dyne
Answer: (b) newton
Q2. Newton’s first law of motion is also known as the:
(a) law of force (b) law of inertia (c) law of action-reaction (d) law of momentum
Answer: (b) law of inertia
Q3. The momentum of a body of mass 2 kg moving with velocity 5 m/s is:
(a) 2.5 kg·m/s (b) 7 kg·m/s (c) 10 kg·m/s (d) 25 kg·m/s
Answer: (c) 10 kg·m/s
Q4. Which of the following has the largest inertia?
(a) An eraser (b) A school bag (c) A loaded truck (d) A cricket ball
Answer: (c) A loaded truck
Q5. A force of 10 N acts on a body of mass 2 kg. The acceleration produced is:
(a) 2 m/s² (b) 5 m/s² (c) 10 m/s² (d) 20 m/s²
Answer: (b) 5 m/s²
Q6. Action and reaction forces:
(a) act on the same body (b) act on different bodies (c) are unequal (d) act in the same direction
Answer: (b) act on different bodies
Q7. The product of force and time is called:
(a) momentum (b) impulse (c) acceleration (d) work
Answer: (b) impulse
Q8. Conservation of momentum is a direct consequence of:
(a) Newton’s first law (b) Newton’s second law (c) Newton’s third law (d) Law of gravitation
Answer: (c) Newton’s third law
Q9. When a bus suddenly starts moving, passengers fall:
(a) forward (b) backward (c) sideways (d) downward
Answer: (b) backward (due to inertia of rest)
Q10. 1 N is equivalent to:
(a) 1 kg·m/s (b) 1 kg·m/s² (c) 1 kg/m·s (d) 1 kg·m²/s
Answer: (b) 1 kg·m/s²
Fill in the Blanks
Q1. The natural tendency of a body to resist change in its state of rest or motion is called __________.
Answer: inertia
Q2. The mathematical form of Newton’s second law of motion is __________.
Answer: F = ma
Q3. Momentum is the product of __________ and __________.
Answer: mass and velocity
Q4. The forces whose net effect is zero are called __________ forces.
Answer: balanced
Q5. The action and reaction always act on __________ bodies.
Answer: two different
True or False
Q1. A body cannot have momentum without having velocity.
Answer: True
Q2. Inertia depends on the volume of the body.
Answer: False (inertia depends on mass)
Q3. The momentum of a system of two colliding bodies remains constant in the absence of an external force.
Answer: True
Q4. Action and reaction can cancel each other.
Answer: False (they act on different bodies, hence cannot cancel)
Q5. A rocket works on the principle of conservation of momentum.
Answer: True
Glossary
| Term | Meaning |
|---|---|
| Force | A push or pull that changes the state of rest or motion of a body. |
| Balanced Force | Forces whose net resultant is zero; produces no acceleration. |
| Unbalanced Force | Forces with a non-zero resultant; produces acceleration. |
| Inertia | Tendency of a body to resist change in its state of rest or motion. |
| Inertia of Rest | Tendency of a body at rest to remain at rest. |
| Inertia of Motion | Tendency of a moving body to keep moving uniformly. |
| Inertia of Direction | Tendency of a body to keep moving in the same direction. |
| Momentum | Product of mass and velocity (p = mv); a vector quantity. |
| Impulse | Product of force and time of action; equal to change in momentum. |
| Newton (N) | SI unit of force; force that gives 1 kg an acceleration of 1 m/s². |
| Action-Reaction | Equal and opposite forces acting on two different bodies. |
| Conservation of Momentum | Total momentum of an isolated system remains constant. |
| Recoil | Backward motion of a gun when a bullet is fired forward. |
Important Formulae
| Quantity | Formula | SI Unit |
|---|---|---|
| Momentum (p) | p = mv | kg·m/s |
| Force (Newton’s 2nd Law) | F = ma = (mv − mu)/t | newton (N) |
| Acceleration (a) | a = F/m = (v − u)/t | m/s² |
| Impulse (J) | J = F·t = Δp = m(v − u) | N·s or kg·m/s |
| Conservation of Momentum | m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ | kg·m/s |
| Recoil Velocity | V = −(m·v)/M | m/s |
| Definition of 1 N | 1 N = 1 kg × 1 m/s² | kg·m/s² |
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