NCERT Solutions for Class 11 Physics Chapter 4 – Laws of Motion

Laws of Motion is a core and high-weightage chapter in Class 11 Physics that forms the backbone of mechanics. This chapter explains Newton’s three laws of motion, inertia, force, momentum, impulse, friction, and circular motion. A strong understanding of this chapter is essential for solving numerical problems in higher classes and for competitive exams like JEE and NEET.

NCERT Solutions for Class 11 Physics Chapter 4 – Laws of Motion are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with free-body diagrams and solved numericals, helping students build conceptual clarity, apply laws correctly, and perform well in school exams and entrance exams.

NCERT Solutions for Class 11 Physics Chapter 4 – Laws of Motion

Laws of Motion

Medium

Q.

Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg,
(a) Just after it is dropped from the window of a stationary train,
(b) Just after it is dropped from the window of a train running at a constant velocity of 36 kmh^-1,
(c) Just after it is dropped from the window of a train accelerating with 1 ms^-2,
(d) Lying on the floor of a train which is acceleration with 1, the stone being at rest relative to the train. Neglect the resistance of air throughout.

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Laws of Motion

Medium

Q.

A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in Fig. 5.19. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of 700 N, which mode should the man adopt to lift the block without the floor yielding?

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Laws of Motion

Easy

Q.

A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev min^-1. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

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Laws of Motion

Easy

Q.

You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘death well’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m?

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{A disc revolves with a speed of 33}\frac{\text{1}}{\text{3}}\text{rev/min, and has a radius of 15 cm}\text{. Two coins are placed at 4 cm and 14 cm away from the centre of the }\\ \text{record}\text{. If the co-efficient of friction between the coins and the record is 0}\text{.15, which of the coins will revolve}\text{with the record?}\end{array}$

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Laws of Motion

Difficult

Q.

$\begin{array}{l}\text{The rear side of a truck is open and a box of 40 kg mass is}\text{placed 5 m away from}\text{the open end as shown in Fig}\text{. 5}\text{.22}\text{. }\\ \text{The coefficient of friction between the box and}\text{the surface below it is 0}\text{.15}\text{. On}\text{a straight road,}\text{the truck starts from rest and}\\ {\text{accelerates with 2 ms}}^{\text{–2}}\text{.At what distance from the starting point does the box fall}\text{off the truck?}\\ \text{(Ignore the size of the box)}\end{array}$

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{A block of mass 15 kg is placed on a long trolley}\text{. The coefficient of static friction}\text{between the block and the trolley is 0}\text{.18}\text{. }\\ \text{The trolley accelerates from rest with 0}{\text{.5m s}}^{\text{–2}}\text{for 20 s and then moves with uniform velocity}\text{. Discuss the motion of the }\\ \text{block as viewed by }\left(\text{a}\right)\text{ a stationary observer on the ground,}\left(\text{b}\right)\text{ an observer moving with}\text{the trolley}\text{.}\end{array}$

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{Two bodies A and B of masses 5 kg and 10 kg in contact with each}\\ \text{other rest on a}\text{table against a rigid wall }\left(\text{Fig}\text{. 5}\text{.21}\right)\text{.}\\ \text{The coefficient of friction between the bodies}\text{and the}\text{table is 0}\text{.15}\text{.}\\ \text{A force of 200 N is applied horizontally to A}\text{. What are}\\ \left(\text{a}\right)\text{ the}\text{reaction of the partition }\\ \left(\text{b}\right)\text{ the action-reaction forces between A and B?}\text{What}\text{happens when}\\ \text{the wall is removed? Does the answer to }\left(\text{b}\right)\text{ change, when the bodies}\\ \text{are in motion? Ignore the difference between }{\mu }_{\text{s}}\text{ and }{\mu }_{\text{k}}.\end{array}$

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{A monkey of mass 40 kg climbs on a rope }\left(\text{Fig}\text{. 5}\text{.20}\right)\text{which can stand a maximum}\text{tension of 600 N}\text{.}\\ \text{In which of the following cases will the rope break: the monkey}\\ \left(\text{a}\right){\text{ climbs up with an acceleration of 6 m s}}^{\text{–2}}\\ \left(\text{b}\right){\text{ climbs down with an acceleration of 4 m s}}^{\text{–2}}\\ \left(\text{c}\right){\text{ climbs up with a uniform speed of 5 m s}}^{\text{–1}}\\ \left(\text{d}\right)\text{ falls down the rope nearly freely under gravity?}\\ \left(\text{Ignore the mass of the rope}\right)\text{.}\end{array}$

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Laws of Motion

Medium

Q.

A train runs along an unbanked circular track of radius 30 m at a speed of 54 kmh^-1.The mass of the train is 106 kg. What provides the centripetal force required for this purpose – The engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{One end of a string of length r is connected to a particle of mass m}\\ \text{and the other end to a small peg}\text{on}\text{a}\text{smooth}\text{horizontal}\text{surface}\text{. }\\ \text{If}\text{the}\text{particle}\text{moves}\text{in}\text{a}\text{circle}\text{with}\text{speed}\text{v,}\text{the}\text{net}\text{force}\text{on}\text{the}\\ \text{particle}\text{(directed}\text{towards}\text{centre)}\text{is}\\ \text{(i)}\text{T}\text{(ii)}\text{T -}\frac{{\text{mv}}^{\text{2}}}{\text{r}}\text{(ii)}\text{T +}\frac{{\text{mv}}^{\text{2}}}{\text{r}}\text{(iv)}\text{0}\end{array}$

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Laws of Motion

Medium

Q.

An aircraft executes a horizontal loop speed of 720 kmh^-1 with its wings banked at 15^°. What is the radius of the loop?

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{Ten one - rupee coins are put on top of each other on a table}\text{. Each coin has a mass}\text{m}\text{. Give the magnitude and direction of}\\ \left(\text{a}\right){\text{ the force on the 7}}^{\text{th}}\text{ coin (counted from the bottom)}\text{due to all the coins on its}\text{top,}\\ \left(\text{b}\right){\text{ the force on the 7}}^{\text{th}}\text{ coin by the eighth coin,}\\ \left(\text{c}\right){\text{ the reaction of the 6}}^{\text{th}}{\text{ coin on the 7}}^{\text{th}}\text{ coin}\text{.}\end{array}$

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{A stream of water flowing horizontally with a speed of 15}{\text{ms}}^{\text{–1}}\text{ pushes out of a tube}\text{of cross}\\ {\text{-sectional area 10}}^{\text{–2}}{\text{m}}^{\text{2}}\text{, and hits a vertical wall nearby}\text{. What is the force}\text{exerted on the wall }\\ \text{by the impact of water, assuming it does not rebound?}\end{array}$

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{A stone of mass m tied to the end of a string revolves in a vertical}\\ \text{circle of radius R}\text{.}\text{The net forces at the lowest and highest points}\\ \text{of the circle directed vertically downwards are: }\\ \left[\text{Choose the correct alternative}\right]\\ \text{Lowest Point}\text{Highest Point}\\ \left(\text{a}\right)\text{ mg}–{\text{T}}_{\text{1}}\text{mg}+{\text{T}}_{\text{2}}\\ \left(\text{b}\right)\text{ mg}+{\text{T}}_{\text{1 }}\text{mg}–{\text{T}}_{\text{2}}\\ \left(\text{c}\right)\text{ mg}+{\text{T}}_{\text{1}}–\left(m{v}_1^2\right)/\text{R }\text{mg}–{\text{T}}_{\text{2}}+\left(m{v}_1^2\right)/\text{R}\\ \left(\text{d}\right)\text{ mg}–{\text{T}}_{\text{1}}–\left(m{v}_1^2\right)/\text{R }\text{mg}+{\text{T}}_{\text{2}}+\left(m{v}_1^2\right)/\text{R}\\ {\text{T}}_{\text{1}}{\text{ and v}}_{\text{1}}\text{ denote the tension and speed at the lowest point}\text{.}\\ {\text{T}}_{\text{2}}{\text{ and v}}_{\text{2}}\text{ denote}\text{corresponding values at the highest point}\text{.}\end{array}$

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{Figure 5}\text{.18 shows a man standing stationary withrespect to a}\\ \text{horizontal conveyor belt that is accelerating}{\text{with 1 m s}}^{\text{-2}}\text{.}\\ \text{What}\text{is the net force on the man? If the coefficient of static}\\ \text{friction between the man's shoes and the belt is 0}\text{.2,}\\ \text{up to what}\text{acceleration of the belt can the man continue}\\ \text{to}\text{be stationary}\text{relative to the belt? (Mass of the man = 65 kg}\text{.)}\end{array}$

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Laws of Motion

Medium

Q.

Figure 5.17 shows the position-time graph of a particle of mass 0.04 kg. Suggest a suitable physical context for this motion. What is the time between two consecutive impulses received by the particle? What is the magnitude of each impulse?

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Laws of Motion

Medium

Q.

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev. min^-1 in a horizontal plane. What is the tension in the string?
What is the maximum speed with which the stone can be whirled around if the string can with stand a maximum tension of 200 N?

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Laws of Motion

Medium

Q.

A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 kmh-¹. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)

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Laws of Motion

Medium

Q.

$\begin{array}{l}\text{A thin circular loop of radius R rotates about its vertical diameter}\\ \text{with an angular}\text{frequency }\omega .\text{ Show that a small bead on the wire}\\ \text{loop}\text{remains at its lowermost point}\text{for}\omega \le \sqrt{\frac{g}{R}}.\text{What is the angle}\\ \text{made by the radius vector joining the centre to the}\text{bead with the}\\ \text{vertical downward direction for}\omega \text{=}\sqrt{\frac{2g}{R}}\text{ ? Neglect friction}\text{.}\end{array}$

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Q1. What is inertia? Explain its types with examples.

Answer:
Inertia is the natural tendency of a body to resist any change in its state of rest or uniform motion.

Types of inertia:

1. Inertia of rest: A book lying on a table remains at rest unless an external force is applied.

2. Inertia of motion: A moving bus continues to move unless brakes are applied.

3. Inertia of direction: Passengers lean sideways when a car takes a sharp turn.

Q2. State Newton’s First Law of Motion and explain its significance.

Answer:
Newton’s First Law states that a body remains at rest or continues in uniform straight-line motion unless acted upon by an external unbalanced force.

Significance:

• Introduces the concept of force

• Explains inertia

• Defines inertial frames of reference

Q3. Define momentum. Write its SI unit and dimensional formula.

Answer:
Momentum is defined as the product of mass and velocity of a body.

$$p = mv$$

• SI unit: kg m s⁻¹

• Dimensional formula: [M L T⁻¹]

Q4. State Newton’s Second Law of Motion. How does it lead to the definition of force?

Answer:
Newton’s Second Law states that the rate of change of momentum of a body is directly proportional to the applied force and occurs in the direction of force.

$$F = ma$$

This law provides the quantitative definition of force.

Q5. What is impulse? How is it related to change in momentum?

Answer:
Impulse is defined as the product of force and time for which the force acts.

$$Impulse = F \times t = \Delta p$$

Impulse is equal to the change in momentum of the body.

Q6. State Newton’s Third Law of Motion with an example.

Answer:
Newton’s Third Law states that for every action, there is an equal and opposite reaction.

Example:
When a person walks, the foot pushes the ground backward, and the ground pushes the person forward.

Q7. Explain the law of conservation of momentum.

Answer:
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external force acts on it.

This law is derived directly from Newton’s Third Law of Motion.

Q8. Why is it easier to stop a tennis ball than a cricket ball moving with the same speed?

Answer:
Momentum depends on mass and velocity.
Since a cricket ball has greater mass than a tennis ball, it has greater momentum and requires more force to stop.

Q9. What is friction? Mention its advantages and disadvantages.

Answer:
Friction is the force that opposes the relative motion between two surfaces in contact.

Advantages:

• Enables walking

• Helps in writing

• Allows vehicles to move

Disadvantages:

• Causes wear and tear

• Produces heat

• Reduces efficiency

Q10. Explain why seat belts are used in vehicles.

Answer:
Seat belts increase the time taken for a passenger to stop during sudden braking, thereby reducing the force experienced by the body according to Newton’s Second Law.

FAQs: Class 11 Physics Chapter 4 – Laws of Motion

Q1. Why is Laws of Motion important for Class 11 Physics?
It is a foundational chapter required for almost all mechanics topics.

Q2. Which topics are most important in this chapter?
Newton’s laws, friction, free-body diagrams, and circular motion.

Q3. Are numericals frequently asked from this chapter?
Yes, force- and friction-based numericals are very common.

Q4. Is diagram practice necessary?
Yes, free-body diagrams are crucial for correct problem solving.

Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with solved examples.