CBSE Class 11 Physics Newton laws of Motion Exam Notes

Question. In figure:

(A) retardation is uniform
(B) velocity is decreasing with time
(C) beyond M, the body has negative velocity
(D) all the above are incorrect
Answer: D

Question. A player completes a circular path of radius r in 40 s. At the end of 2 mintures 20 seconds, displacement will be:
(A) 2r
(B) 2πr
(C) 7πr
(D) zero
Answer: A

Question. A body whose speed in a particular direction is constant:
(A) must be accelerating
(B) must be retarding
(C) has a constant velocity
(D) all the above
Answer: C

Question. A body moving along a circular path has:
(A) a constant speed
(B) a constant velocity
(C) non tangential velocity
(D) no radial acceleration
Answer: A

Question. In figure BC represents a body moving: 

(A) backward with uniform velocity
(B) forward with uniform velocity
(C) backward with non-uniform velocity
(D) forward with non-uniform velocity
Answer: A

Question. The velocity of a particle increases from u to v in a time t during which it covers a distances S. If the particle has a uniform accelration, which one of the following euqations does not apply to the motion?
(A) 2S = (v + u)t
(B) a = v-u/t
(C) v² = u² – 2 aS
(D) S = (u+1/2 at)t
Answer: C

Question. A body has an acceleration of –4 ms^–2. What is its retardation?
(A) –4 ms²
(B) 4 ms^–2
(C) Zero
(D) Nothing can be decided
Answer: B

Question. A cyclist moves from a certain point X and goes round a circle of radius ‘r’ and reaches Y, exactly at the other side of the point X, as shown in figure.
The displacement of the cyclist would be:

(A) πr
(B) 2πr
(C) 2r
(D) 2π/r
Answer: C

Question. In the above problem, the distance covered by the cyclist would be:
(A) πr
(B) 2πr
(C) 2r
(D) 2π/r
Answer: A

Question. In the above question, the velocity:
(A) increases between points O and A
(B) increases between points A and B
(C) decreases between points A and B
(D) is zero throughout
Answer: B

Question. When a graph between two physical quantities is a straight line, the two quantities are:
(A) both constant
(B) independent of each other
(C) directly proportional
(D) inversely proportional
Answer: C

Question. A man walks 8m towards East and then 6m towards North. His magnitude of displacement is:
(A) 10 m
(B) 14 m
(C) 2 m
(D) zero
Answer: A

Question. Area undera velocity-time graph gives:
(A) the time taken by a moving object
(B) the distance travelled by a moving object
(C) the acceleration of moving object
(D) the retardation of a moving object
Answer: B

Question. In figure, the velocity of the body at A is: 

(A) zero
(B) unity
(C) maximum
(D) infinite
Answer: A

Question. Which of the following relations represents the relationship between the average speed, time and distance correctly?
(A) Average speed = distance × time
(B) Average speed = total distance/total time
(C) Time = average speed + distance
(D) Distance = average speed – time
Answer: B

NEWTON’S LAWS

First Law of Motion: The state of the body can’t be changed until or unless an external force is applied on the body. This statement is applicable in inertial frame of reference only.
This law is also called law of inertia where inertial mass is the quantity of matter in a body and inertia is the property of a body due to which a body resists any change in its state of rest or of uniform motion in a straight line. The larger is the mass of the body, the larger is the tendency to resist any change in its state of rest or of uniform motion in a straight line i.e., resist any change in its velocity. Newton’s first law gives a qualitative definition of force. A force is a push or pull exerted by a body which can accelerate, decelerate or deform a body.

EQUILIBRIUM

If net external concurrent force acting on the body is zero the body is said to be in equilibrium. There are two types of equilibrium
(a) Static equilibrium: When body is at rest under the influence of external forces acting on the body.
(b) Dynamic equilibrium: If net external force is zero but the velocity of body is not zero i.e., body moves with constant velocity.

Second Law of Motion: The rate of change of momentum of a body is directly proportional to the net external force and this rate of change takes place in the direction of the force.
If a particle of mass m is moving with velocity v, its momentum p = mv.
If F is the force applied, F α dp/dt or F = K dp/dt where K is a constant
If the constant K is chosen as unity, (if F in Newton and P in kg.m/s and time t in second then k = 1)
F = dp/dt
The force F is a vector. If mass m is constant and a is acceleration of the body.
dp/dt = m dv/dt= ma, F = ma.

Newton’s Second Law of Motion gives a quantitative measure of force. The unit of force is Newton. A force of 1 Newton produces an acceleration of 1 metre/second2 to a body of mass 1 kg.

INERTIAL AND NON-INERTIAL FRAMES OF REFERENCE

Non accelerated frame of reference are called inertial frame of reference while accelerated frames are called non inertial frame of reference.If one is travelling in a train which is accelerated forward, the body in the train is pushed backwards and he is pushed forward when the brakes are applied due to inertia of the body. Such an accelerated frame is called a non-inertial frame of reference. In order to make Newton’s laws applicable to such a frame, a fictitious inertial force or pseudo force is applied on the body. The magnitude of this pseudo force is equal to the product of the mass m of the body and the acceleration a of the reference frame and its direction is opposite to the acceleration of the frame.
∴ pseudo force, F = –m × a
Thus in non-inertial frame of reference trolley moving with an acceleration, a hanging bob of mass m will be deflected through angle θ due to a pseudo force acting in backward direction. In the noninertial frame of reference, the bob is in equilibrium under the action of force due to tension T, weight mg and the pseudo force ma in a direction making an angle θ with the vertical

Third Law of Motion: Every action has an equal and opposite reaction. Thus if a body A exerts a force on another body B, the second body B exerts an equal and opposite
force, i.e., reaction on the first body A.
∴ FAB = –FBA

FREE BODY DIAGRAM
When all the external forces are indicated on the body it said to be representing free body diagram (F. B. D.) of the body.

NORMAL REACTION
Normal reaction is pressing force between the two surface in contact. It is always directed normal to the contact surface.

• Force is a push or pull upon an object resulting from the object's interaction with another object. The various effects of force are:
• Force can move a body initially at rest.
• Force can bring a moving body to rest.
• Force can change the direction of a moving body.
• Force can change the speed of a moving body.
• Force can change the shape of a body.
• Force can change the size of a body.

Muscular force – It involves the action of muscles.
Animals make use of muscular force to carry out their physical activities and other tasks.

Friction – It is an opposing force that acts between surfaces in contact moving with respect to each other.

• Frictional force always acts between two moving objects, which are in contact with one another.
• Frictional force always acts opposite to the direction of motion.
• Frictional force depends on the nature of the surface in contact.

Tension Force - This force appears in a string, attached to a rigid support, when an object is suspended by it.

Mechanical Force - It involves the force generated by machines.
Force exerted during collision -Two objects push each other with an equal but opposite forces if collision occurs between them. These forces are known as the force of action and force of reaction.

Combined Forces - When two or more forces are acting on the same object.
Non-contact force come into play even when the bodies are not in contact.

Magnetic force – Force acting between two magnets or a magnet and a magnetic material (eg. iron, steel, nickel, cobalt etc.). It can be attractive and repulsive.

Electrostatic force – Force due to electric charges. It can be attractive and repulsive.

Gravitational force – It is a kind of attractive force that comes into play because of the mass of a body. (eg. earth's gravitational attraction).

First law of motion
A body at rest remains at rest and a body in uniform motion continues its uniform motion unless an external force is applied.

Inertia:
It is the tendency of a body to resist any change in its state of rest or of uniform motion along a straight line.
Mass of an object is the measure of its inertia, more is the mass more is the inertia.
Types of inertia: Inertia of rest and motion

Momentum is the product of the mass of the body and its velocity. It is a vector quantity.
Momentum = Mass × Velocity
SI unit of the momentum is kg m/s.

Second law of motion
The second law of motion says, when a force F is subjected to a body of mass m, an acceleration a is gained by the body in the direction of the force and the magnitude of acceleration is directly proportional to the F and inversely proportional to the m.
Rate of change of momentum ∝ Applied unbalanced force

Direction of change in momentum is the same as the direction of unbalanced force

F = ma

Unit of force is Newton
1 N = 1 kg × 1 m / s²

Third law of motion
For every action force there is an equal and opposite reaction force.
The horse and the cart: From the third law of motion the pull by the horse in the forward direction is equal to the pull by the cart in the backward direction. The sum of these forces is therefore zero. Why should then the cart accelerate forward? Apart from the pulls of the horse and the cart there is frictional force and the reaction of the ground on the horse and the cart is also present. The resultant force of this normal reaction and the friction together helps the horse to move the cart in the forward direction.

Universal law of gravitation

For a point mass

The point of attraction between a hollow spherical shell of uniform density and a point mass situated outside is just as if the entire mass of the cell is concentrated at the center of the shell.
The force of attraction due to a hollow spherical shell of uniform density, on a point mass inside it is zero.

Gravitation Constant, G = 6.67 × 10^–11 Nm²/kg² 

Free Fall: A body is said to be free falling if it begins to fall downward towards the earth due to earth’s gravity only.
mg=GMmR2g=GMR2
‘g = 9.8 m/s2’ is the acceleration due to gravity, it is the acceleration of a freely falling body.

Tips to solve numerical
For upward motion take g = –9.8m/s² and final velocity at the highest point as 0.
For downward motion take g = 9.8m/s² and for a freely falling body take initial velocity as 0.

Equations of motion of an object under the influence of the earth’s gravity for downward motion of the particle
v=u+gts=ut+12gt2v2=u2+2gs
for upward motion of the particle
v=u-gts=ut-12gt2v2=u2-2gs

Mass: It is the amount of matter contained in the body
Weight: It is the force exerted on a body due to the gravitational pull of another body such as the earth, the sun etc.