# CBSE Class 11 Physics Chapter 5 Laws of motion Study Materials

### Law of Motion Class 11 Notes Physics Chapter 5

• Dynamics is the branch of physics in which we study the motion of a body by taking into consideration the cause i.e., force which produces the motion.
• Force
Force is an external cause in the form of push or pull, which produces or tries to produce motion in a body at rest, or stops/tries to stop a moving body or changes/tries to change the direction of motion of the body.
• The inherent property, with which a body resists any change in its state of motion is called inertia. Heavier the body, the inertia is more and lighter the body, lesser the inertia.
• Law of inertia states that a body has the inability to change its state of rest or uniform motion (i.e., a motion with constant velocity) or direction of motion by itself.
• Newton’s Laws of Motion
Law 1. A body will remain at rest or continue to move with uniform velocity unless an external force is applied to it.
First law of motion is also referred to as the ‘Law of inertia’. It defines inertia, force and inertial frame of reference.
I here is always a need of ‘frame of reference’ to describe and understand the motion of particle, lhc simplest ‘frame of reference’ used are known as the inertial frames.
A frame of referent, e is known as an inertial frame it, within it, all accelerations of any particle are caused by the action of ‘real forces’ on that particle.
When we talk about accelerations produced by ‘fictitious’ or ‘pseudo’ forces, the frame of reference is a non-inertial one.
Law 2. When an external force is applied to a body of constant mass the force produces an acceleration, which is directly proportional to the force and inversely proportional to the mass of the body.

Law 3. “To every action there is equal and opposite reaction force”. When a body A exerts a force on another body B, B exerts an equal and opposite force on A.
• Linear Momentum
The linear momentum of a body is defined as the product of the mass of the body and its velocity.

• Impulse
Forces acting for short duration are called impulsive forces. Impulse is defined as the product of force and the small time interval for which it acts. It is given by

Impulse of a force is a vector quantity and its SI unit is 1 Nm.
— If force of an impulse is changing with time, then the impulse is measured by finding the area bound by force-time graph for that force.
— Impulse of a force for a given time is equal to the total change in momentum of the body during the given time. Thus, we have

• Law of Conservation of Momentum
The total momentum of an isolated system of particles is conserved.
In other words, when no external force is applied to the system, its total momentum remains constant.

• Recoiling of a gun, flight of rockets and jet planes are some simple applications of the law of conservation of linear momentum.

• Concurrent Forces and Equilibrium
“A group of forces which are acting at one point are called concurrent forces.”
Concurrent forces are said to be in equilibrium if there is no change in the position of rest or the state of uniform motion of the body on which these concurrent forces are acting.
For concurrent forces to be in equilibrium, their resultant force must be zero. In case of three concurrent forces acting in a plane, the body will be in equilibrium if these three forces may be completely represented by three sides of a triangle taken in order. If number of concurrent forces is more than three, then these forces must be represented by sides of a closed polygon in order for equilibrium.
• Commonly Used Forces
(i) Weight of a body. It is the force with which earth attracts a body towards its centre. If M is mass of body and g is acceleration due to gravity, weight of the body is Mg in vertically downward direction.
(ii) Normal Force. If two bodies are in contact a contact force arises, if the surface is smooth the direction of force is normal to the plane of contact. We call this force as Normal force.
Example. Let us consider a book resting on the table. It is acted upon by its weight in vertically downward direction and is at rest. It means there is another force acting on the block in opposite direction, which balances its weight. This force is provided by the table and we call it as normal force.
(iii) Tension in string. Suppose a block is hanging from a string. Weight of the block is acting vertically downward but it is not moving, hence its weight is balanced by a force due to string. This force is called ‘Tension in string’. Tension is a force in a stretched string. Its direction is taken along the string and away from the body under consideration.

• Simple Pulley
Consider two bodies of masses m1 and m2 tied at the ends of an in extensible string, which passes over a light and friction less pulley. Let m1 > m2. The heavier body will move downwards and the lighter will move upwards. Let a be the common acceleration of the system of two bodies, which is given by

• Apparent Weight and Actual Weight
— ‘Apparent weight’ of a body is equal to its ‘actual weight’ if the body is either in a state of rest or in a state of uniform motion.
— Apparent weight of a body for vertically upward accelerated motion is given as
Apparent weight =Actual weight + Ma = M (g + a)
— Apparent weight of a body for vertically downward accelerated motion is given as
Apparent weight = Actual weight Ma = M (g – a).
• Friction
The opposition to any relative motion between two surfaces in contact is referred to as friction. It arises because of the ‘inter meshing’ of the surface irregularities of the two surfaces in contact.
• Static and Dynamic (Kinetic) Friction
The frictional forces between two surfaces in contact (i) before and (ii) after a relative motion between them has started, are referred to as static and dynamic friction respectively. Static friction is always a little more than dynamic friction.
The magnitude of kinetic frictional force is also proportional to normal force.
• Limiting Frictional Force
This frictional force acts when body is about to move. This is the maximum frictional force that can exist at the contact surface. We calculate its value using laws of friction.
Laws of Friction:
(i) The magnitude of limiting frictional force is proportional to the normal force at the contact surface.

(ii) The magnitude of limiting frictional force is independent of area of contact between the surfaces.
• Coefficient of Friction
The coefficient of friction (μ) between two surfaces is the ratio of their limiting frictional force to the normal force between them, i.e.,

• Angle of Friction
It is the angle which the resultant of the force of limiting friction F and the normal reaction R makes with the direction of the normal reaction. If θ is the angle of friction, we have

• Angle of Repose
Angle of repose (α) is the angle of an inclined plane with the horizontal at which a body placed over it just begins to slide down without any acceleration. Angle of repose is given by α = tan-1 (μ)
• Motion on a Rough Inclined Plane
Suppose a motion up the plane takes place under the action of pull P acting parallel to the plane.
• Centripetal Force
Centripetal force is the force required to move a body uniformly in a circle. This force acts along the radius and towards the centre of the circle. It is given by

where, v is the linear velocity, r is the radius of circular path and ω is the angular velocity of the body.
• Centrifugal Force
Centrifugal force is a force that arises when a body is moving actually along a circular path, by virtue of tendency of the body to regain its natural straight line path.
The magnitude of centrifugal force is same as that of centripetal force.

• Motion in a Vertical Circle
The motion of a particle in a horizontal circle is different from the motion in vertical circle. In horizontal circle, the motion is not effected by the acceleration due to gravity (g) whereas in the motion of vertical circle, the motion is not effected by the acceleration due to gravity (g) whereas in the motion of vertical circle, the value of ‘g’ plays an important role, the motion in this case does not remain uniform. When the particle move up from its lowest position P, its speed continuously decreases till it reaches the highest point of its circular path. This is due to the work done against the force of gravity. When the particle moves down the circle, its speed would keep on increasing.

Let us consider a particle moving in a circular vertical path of radius V and centre o tide with a string. L be the instantaneous position of the particle such that

Here the following forces act on the particle of mass ‘m’.
(i) Its weight = mg (verticaly downwards).
(ii) The tension in the string T along LO.

We can take the horizontal direction at the lowest point ‘p’ as the position of zero gravitational potential energy. Now as per the principle of conservation of energy,

From this relation, we can calculate the tension in the string at the lowest point P, mid-way point and at the highest position of the moving particle.
Case (i) : At the lowest point P, θ = 0°
When the particle completes its motion along the vertical circle, it is referred to as “Looping the Loop” for this the minimum speed at the lowest position must be √5gr
• IMPORTANT TABLES

### CBSE Class 11 Physics Chapter-5 Important Questions

1 Marks Questions

1.What is the unit of coefficient of friction?

Ans: It has no unit.

2.Name the factor on which coefficient of friction depends?

Ans:Coefficient of friction  depends on the nature of surfaces in contact and nature of motion.

3.What provides the centripetal force to a car taking a turn on a level road?

Ans: Centripetal force is provided by the force of friction between the tyres and the road.

4.Why is it desired to hold a gun tight to one’s shoulder when it is being fired?

Ans: Since the gun recoils after firing so it must be held lightly against the shoulder because gun and the shoulder constitute one system of greater mass so the back kick will be less.

5.Why does a swimmer push the water backwards?

Ans: A swimmer pushes the water backwards because due to reaction of water he is able to swim in the forward direction

6.Friction is a self adjusting force. Justify.

Ans: Friction is a self adjusting force as its value varies from zero to the maximum value to limiting friction.

7.A thief jumps from the roof of a house with a box of weight W on his head. What will be the weight of the box as experienced by the thief during jump?

Ans: Weight of the box W = m (g – a) = m (g – g) = 0.

8.Which of the following is scalar quantity? Inertia, force and linear momentum.

Ans:Inertia and linear momentum is measured by mass of the body and is a vector quantity and mass is a scalar quantity.

9.Action and reaction forces do not balance each other. Why?

Ans:Action and reaction do not balance each other because a force of action and reaction acts always on two different bodies.

10.If force is acting on a moving body perpendicular to the direction of motion, then what will be its effect on the speed and direction of the body?

Ans:No change in speed, but there can be change in the direction of motion.

11.The two ends of spring – balance are pulled each by a force of 10kg.wt. What will be the reading of the balance?

Ans:The reading of the balance will be 10kgwt.

12.A lift is accelerated upward. Will the apparent weight of a person inside the lift increase, decrease or remain the same relative to its real weight? If the lift is going with uniform speed, then?

Ans:The apparent weight will increase. If the lift is going with uniform speed, then the apparent weight will remain the same as the real weight.

14. If, in Exercise 5.21, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks:

(a) the stone moves radially outwards,

(b) the stone flies off tangentially from the instant the string breaks,

(c) the stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle ?

Ans.(b)When the string breaks, the stone will move in the direction of the velocity at that instant. According to the first law of motion, the direction of velocity vector is tangential to the path of the stone at that instant. Hence, the stone will fly off tangentially from the instant the string breaks.

2 Marks Questions

1.Give the magnitude and direction of the net force acting on

(a) A drop of rain falling down with constant speed.

(b) A kite skillfully held stationary in the sky.

Ans: (1) According to first law of motion F = 0 as a = 0 (particle moves with constant speed)

(2) Since kite is stationary net force on the kite is also zero.

4.A force is being applied on a body but it causes no acceleration. What possibilities may be considered to explain the observation?

Ans: (1) If the force is deforming force then it does not produce acceleration.

(2) The force is internal force which cannot cause acceleration.

5.Force of 16N and 12N are acting on a mass of 200kg in mutually perpendicular directions. Find the magnitude of the acceleration produced?

Ans:

6.An elevator weighs 3000kg. What is its acceleration when the in the tension supporting cable is 33000N. Given that g = 9.8m/s2.

Ans:Net upward force on the

ElevatorF = T – mg

7.Write two consequences of Newton’s second law of motion?

Ans: (1) It shows that the motion is accelerated only when force is applied.

(2) It gives us the concept of inertial mass of a body.

8.A bird is sitting on the floor of a wire cage and the cage is in the hand of a boy. The bird starts flying in the cage. Will the boy experience any change in the weight of the cage?

Ans:When the bird starts flying inside the cage the weight of bird is no more experienced as air inside is in free contact with atmospheric air hence the cage will appear lighter.

9.Why does a cyclist lean to one side, while going along curve? In what direction does he lean?

Ans:A cyclist leans while going along curve because a component of normal reaction of the ground provides him the centripetal force he requires for turning.

He has to lean inwards from his vertical position i.e. towards the centre of the circular path.

10.How does banking of roads reduce wear and tear of the tyres?

Ans:When a curved road is unbanked force of friction between the tyres and the road provides the necessary centripetal force. Friction has to be increased which will cause wear and tear. But when the curved road is banked, a component of normal reaction of the ground provides the necessary centripetal force which reduces the wear and tear of the tyres.

12.A soda water bottle is falling freely. Will the bubbles of the gas rise in the water of the bottle?

Ans:bubbles will not rise in water because water in freely falling bottle is in the state of weight – lessens hence no up thrust force acts on the bubbles.

13.Two billiard balls each of mass 0.05kg moving in opposite directions with speed 6m/s collide and rebound with the same speed. What is the impulse imparted to each ball due to other.

Ans:Initial momentum to the ball A = 0.05(6) = 0.3 kg m/s

As the speed is reversed on collision,

final momentum of ball A = 0.05(-6) = -0.3 kg m/s

Impulse imparted to ball A = change in momentum of ball A = final momentum – initial momentum = -0.3 -0.3 = -0.6 kg m/s.

15.Explain why passengers are thrown forward form their seats when a speeding bus stops suddenly.

Ans:When the speeding bus stops suddenly, lower part of the body in contact with the seat comes to rest but the upper part of the body of the passengers tends to maintain its uniform motion. Hence the passengers are thrown forward.

Scroll to Top