Physics · Class 11 Science
Ch 5Laws of Motion — Class 11 Physics, concept-first.
In the previous chapter, we developed a complete language for describing motion — position, velocity, acceleration — all in quantitative terms. Uniform motion required only the concept of velocity; non-uniform motion brought in acceleration. But description is not explanation.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Newton's First Law
Imagine you're sitting in a bus that's stopped at a signal. The bus suddenly lurches forward. What happens to you? You jerk backwards against the seat.
Most relevant Q&A
- An astronaut accidentally gets separated out of his small spaceship accelerating in interstellar space at a constant rate of $100\ \text{m s…Preview
- Give the magnitude and direction of the net force acting on (a) a drop of rain falling down with a constant speed, (b) a cork of mass $10\ \…Free
- A person driving a car suddenly applies the brakes on seeing a child on the road ahead. If he is not wearing seat belt, he falls forward and…Preview
In previous exams
How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
In the previous chapter, we developed a complete language for describing motion — position, velocity, acceleration — all in quantitative terms.
Aristotle's Fallacy
The question seems simple: why does a moving object eventually stop? A child pulling a toy car knows that if she lets go of the string, the car rolls a little and then stops.
The Law of Inertia
Before Newton, the prevailing view of motion — inherited from Aristotle — held that a force was needed to keep a body moving.
Newton's First Law of Motion
The story of the first law begins with Galileo’s demolition of the Aristotelian view that a force is needed to keep a body in motion.
Newton's Second Law of Motion
3 QThe first law told us what happens when no net external force acts — the body stays at rest or moves uniformly. But the interesting cases in physics involve forces.
+−Worked Examplesi1 question
+−Worked Examplesi1 question
Newton's Third Law of Motion
The second law tells us how a force changes a body's motion, but it leaves a deeper question unanswered: where does that external force come from? Newtonian mechanics gives a simple, consistent answer…
Conservation of Momentum
Newton’s second law tells us that a net external force is needed to change an object’s momentum. The natural flip side of this is: if no net external force acts on a system, its total momentum cannot…
Equilibrium of a Particle
A particle is said to be in equilibrium when the net external force acting on it is zero. This is the most fundamental condition — if the vector sum of all forces vanishes, the particle's state of mot…
Common Forces in Mechanics
In mechanics, we deal with several kinds of forces. The gravitational force is everywhere — every object on Earth experiences it, and it governs the motion of planets and stars.
Friction
3 QWhen a body rests on a horizontal table, two vertical forces balance: the weight downward and the normal reaction upward. Now apply a small horizontal force to the body.
+−Worked Examplesi1 question
+−Worked Examplesi1 question
Circular Motion
2 QFrom Chapter 3, we already know that a body moving in a circle of radius with uniform speed experiences an acceleration directed toward the centre.
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Solving Problems in Mechanics
The three laws of motion form the complete foundation of mechanics. With them, you can handle a vast range of problems — but a typical problem rarely involves a single isolated body under known forces…
Summary
- Newton’s First Law (Law of Inertia): A body at rest stays at rest, and a body in uniform motion stays in uniform motion, unless acted upon by a net external force.
Points to Ponder
1. Force does not have to point in the same direction as velocity. It can be along , opposite to it, perpendicular to it, or at any other angle.
Exercises
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- 4.1Give the magnitude and direction of the net force acting on (a) a drop of rain falling down with a constant speed, (b) a cork of mass $10\ \…Free
- 4.2A pebble of mass $0.05\ \text{kg}$ is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (a) during…Free
- 4.3Give the magnitude and direction of the net force acting on a stone of mass $0.1\ \text{kg}$, (a) just after it is dropped from the window o…Free
- 4.4One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the p…Preview
- 4.5A constant retarding force of $50\ \text{N}$ is applied to a body of mass $20\ \text{kg}$ moving initially with a speed of $15\ \text{m s}^{…Preview
- 4.6A constant force acting on a body of mass $3.0\ \text{kg}$ changes its speed from $2.0\ \text{m s}^{-1}$ to $3.5\ \text{m s}^{-1}$ in $25\ \…Preview
- 4.7A body of mass $5\ \text{kg}$ is acted upon by two perpendicular forces $8\ \text{N}$ and $6\ \text{N}$. Give the magnitude and direction of…Preview
- 4.8The driver of a three-wheeler moving with a speed of $36\ \text{km/h}$ sees a child standing in the middle of the road and brings his vehicl…Preview
- 4.9A rocket with a lift-off mass $20{,}000\ \text{kg}$ is blasted upwards with an initial acceleration of $5.0\ \text{m s}^{-2}$. Calculate the…Preview
- 4.10A body of mass $0.40\ \text{kg}$ moving initially with a constant speed of $10\ \text{m s}^{-1}$ to the north is subject to a constant force…Preview
- 4.11A truck starts from rest and accelerates uniformly at $2.0\ \text{m s}^{-2}$. At $t = 10\ \text{s}$, a stone is dropped by a person standing…Preview
- 4.12A bob of mass $0.1\ \text{kg}$ hung from the ceiling of a room by a string $2\ \text{m}$ long is set into oscillation. The speed of the bob…Preview
- 4.13A man of mass $70\ \text{kg}$ stands on a weighing scale in a lift which is moving (a) upwards with a uniform speed of $10\ \text{m s}^{-1}$…Preview
- 4.14A particle of mass $4\ \text{kg}$ moves along a straight line (one-dimensional motion). Its position $x$ (in metres) varies with time $t$ (i…Preview
- 4.15Two bodies of masses $10\ \text{kg}$ and $20\ \text{kg}$ respectively kept on a smooth, horizontal surface are tied to the ends of a light s…Preview
- 4.16Two masses $8\ \text{kg}$ and $12\ \text{kg}$ are connected at the two ends of a light inextensible string that goes over a frictionless pul…Preview
- 4.17A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in o…Preview
- 4.18Two billiard balls each of mass $0.05\ \text{kg}$ moving in opposite directions with speed $6\ \text{m s}^{-1}$ collide and rebound with the…Preview
- 4.19A shell of mass $0.020\ \text{kg}$ is fired by a gun of mass $100\ \text{kg}$. If the muzzle speed of the shell is $80\ \text{m s}^{-1}$, wh…Preview
- 4.20A batsman deflects a ball by an angle of $45^{\circ}$ without changing its initial speed which is equal to $54\ \text{km/h}$. What is the im…Preview
- 4.21A stone of mass $0.25\ \text{kg}$ tied to the end of a string is whirled round in a circle of radius $1.5\ \text{m}$ with a speed of $40\ \t…Preview
- 4.22If, in Exercise 4.21, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the…Preview
- 4.23Explain why (a) a horse cannot pull a cart and run in empty space, (b) passengers are thrown forward from their seats when a speeding bus st…Preview
Exemplar Problems
Higher-order thinking / exemplar-style practice problems.
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- Q1A ball is travelling with uniform translatory motion. This means that (a) it is at rest. (b) the path can be a straight line or circular and…Free
- Q2A metre scale is moving with uniform velocity. This implies (a) the force acting on the scale is zero, but a torque about the centre of mass…Free
- Q3A cricket ball of mass 150 g has an initial velocity $\mathbf{u} = (3\hat{i} + 4\hat{j})$ m s$^{-1}$ and a final velocity $\mathbf{v} = -(3\…Free
- Q4In the previous problem (5.3), the magnitude of the momentum transferred during the hit is (a) Zero (b) $0.75$ kg m s$^{-1}$ (c) $1.5$ kg m…Preview
- Q5Conservation of momentum in a collision between particles can be understood from (a) conservation of energy. (b) Newton's first law only. (c…Preview
- Q6A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player…Preview
- Q7A body of mass 2kg travels according to the law $x(t) = pt + qt^2 + rt^3$ where $p = 3$ m s$^{-1}$, $q = 4$ m s$^{-2}$ and $r = 5$ m s$^{-3}…Preview
- Q8A body with mass 5 kg is acted upon by a force $\mathbf{F} = (-3\hat{i} + 4\hat{j})$ N. If its initial velocity at $t = 0$ is $\mathbf{v} =…Preview
- Q9A car of mass $m$ starts from rest and acquires a velocity along east $\mathbf{v} = v\hat{i}\,(v > 0)$ in two seconds. Assuming the car move…Preview
- Q10The motion of a particle of mass $m$ is given by $x = 0$ for $t < 0$ s, $x(t) = A \sin 4p\,t$ for $0 < t < (1/4)$ s ($A > o$), and $x = 0$ f…Preview
- Q11A small block A of mass $m/2$ rests on top of a larger block B of mass $m$, and B rests on a horizontal floor. The coefficient of friction b…Preview
- Q12A block of mass $m_1$ rests on an incline that makes an angle $\theta$ with the horizontal. A light string tied to $m_1$ runs up along the s…Preview
- Q13Two inclined planes meet at a common apex where a frictionless pulley is mounted. On the left plane, which makes an angle $\theta_1$ with th…Preview
- Q14Two billiard balls A and B, each of mass 50g and moving in opposite directions with speed of $5$ m s$^{-1}$ each, collide and rebound with t…Preview
- Q15A body of mass 10kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is (Note: more than one of…Preview
- Q16A girl riding a bicycle along a straight road with a speed of $5$ m s$^{-1}$ throws a stone of mass 0.5 kg which has a speed of $15$ m s$^{-…Preview
- Q17A person of mass 50 kg stands on a weighing scale on a lift. If the lift is descending with a downward acceleration of $9$ m s$^{-2}$, what…Preview
- Q18The position–time graph of a body of mass $2\ \text{kg}$ is a straight line rising from the origin: its position $x$ increases uniformly fro…Preview
- Q19A person driving a car suddenly applies the brakes on seeing a child on the road ahead. If he is not wearing seat belt, he falls forward and…Preview
- Q20The velocity of a body of mass 2 kg as a function of $t$ is given by $\mathbf{v}(t) = 2t\,\hat{i} + t^2\,\hat{j}$. Find the momentum and the…Preview
- Q21A block placed on a rough horizontal surface is pulled by a horizontal force $F$. Let $f$ be the force applied by the rough surface on the b…Preview
- Q22Why are porcelain objects wrapped in paper or straw before packing for transportation?Preview
- Q23Why does a child feel more pain when she falls down on a hard cement floor, than when she falls on the soft muddy ground in the garden?Preview
- Q24A woman throws an object of mass 500 g with a speed of 25 m s$^{1}$. (a) What is the impulse imparted to the object? (b) If the object hits…Preview
- Q25Why are mountain roads generally made winding upwards rather than going straight up?Preview
- Q26A block of mass $2\ \text{kg}$ hangs from a rigid ceiling by a thread AB (end A tied to the ceiling, end B tied to the top of the block). An…Preview
- Q27In the above given problem if the lower thread is pulled with a jerk, what happens?Preview
- Q28A block of mass $5\ \text{kg}$ hangs from the ceiling by a light inextensible string, whose tension is $T_1$. A second light inextensible st…Preview
- Q29Block A, of weight $100\ \text{N}$, rests on a frictionless inclined plane whose slope makes an angle of $30^\circ$ with the horizontal. A f…Preview
- Q30A block of mass M is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and t…Preview
- Q31A 100 kg gun fires a ball of 1kg horizontally from a cliff of height 500m. It falls on the ground at a distance of 400m from the bottom of t…Preview
- Q32A particle of mass $500\ \text{g}$ moves in a plane, and its motion is described by two graphs. In the first graph, the $x$-coordinate versu…Preview
- Q33A person in an elevator accelerating upwards with an acceleration of $2$ m s$^{-2}$, tosses a coin vertically upwards with a speed of 20 m s…Preview
- Q34There are three forces $\mathbf{F}_1$, $\mathbf{F}_2$ and $\mathbf{F}_3$ acting on a body, all acting on a point P on the body. The body is…Preview
- Q35When a body slides down from rest along a smooth inclined plane making an angle of $45^\circ$ with the horizontal, it takes time $T$. When t…Preview
- Q36A body of unit mass ($1\ \text{kg}$) moves in a plane, described by two velocity–time graphs. The $x$-velocity graph is triangular: $v_x$ ri…Preview
- Q37A racing car runs on an unbanked closed track ABCDEFA made of two concentric circular arcs joined by two straight radial links, all centred…Preview
- Q38The displacement vector of a particle of mass $m$ is given by $\mathbf{r}(t) = \hat{i}\,A\cos\omega t + \hat{j}\,B\sin\omega t$. (a) Show th…Preview
- Q39A cricket bowler releases the ball in two different ways (a) giving it only horizontal velocity, and (b) giving it horizontal velocity and a…Preview
- Q40Four strings pull on a single point P, which stays at rest (equilibrium). Taking the upward vertical as reference: one string pulls with a f…Preview
- Q41A rectangular box lies on a rough inclined surface. The co-efficient of friction between the surface and the box is $\mu$. Let the mass of t…Preview
- Q42A helicopter of mass 2000kg rises with a vertical acceleration of $15$ m s$^{-2}$. The total mass of the crew and passengers is 500 kg. Give…Preview