force and laws of motion class 9 please consider to follow it gives me education only 1 % of viewers are following its free !

2. What is the cause of motion ??
RECAPITULATION
Motion
Uniform Motion
Non Uniform
Motion
Distance / Displacement
Speed / Velocity
Aceleration
Quantities
Relation between
quantities
Three equation of
Motion
Types
Circular Motion

3. • a push or a pull on an object is called force.

4. A. Gravitational B. Electrostatic C. Magnetic D. Muscular
LETS
POLL!!
Identify the types of forces-
(i) which force always attract objects towards the earth?
(ii) an apple is falling from the tree towards the ground. Which type of force is involved here?
(iii) which force makes a charged comb attracts small pieces ofpaper?

7. What did scientists
say when they
found 2 atoms of
Helium?

8. THEY SAID “HEHE”.

9. MANY PEOPLE HAVE HEARD THIS,
BUT NOBODY HAS EVER SEEN IT.
IT WILL NEVER SPEAK BACK
UNTIL YOU SPEAK TO IT.
What is it?

10. AN ECHO.

11. RESULTANT FORCE
= 3N
= 5N
= 8N
= 3N = 5N
= 2N towardsleft

12. A. 0 N B.2N C. 6 N D. 12 N
1.
III.
1I.
1V.
LETSPOLL !!!!
Find the Net force :
Options:

14. 10. Using a horizontal force of 200 N, we intend to move a wooden cabinet across a floor at a constant velocity. What is
the friction force that will be exerted on the cabinet?
NCERT EXCERCISE
Page 128
4. A batsman hits a cricket ball which then rolls on a level ground. After covering a short distance, the ball comes to
rest. The ball slows to a stop because
(a) the batsman did not hit the ball hard enough.
(b) velocity is proportional to the force exerted on theball.
(c) there is a force on the ball opposing themotion.
(d) there is no unbalanced force on the ball, so the ball would want to come to rest.

15. FORCE
Pull or Push
acting on a body
Balanced Unbalanced
When two forces of
equal magnitude and
in opposite directions
are acting.
Object remains inits
state.
A body changes its position,
speed or direction.
When two or more forces
acting on a body in such a
way that the resultantof all
forces is not zero.
Opposes the motion of anobject
Effect of forces
• Change speed of moving
• Change direction of moving object
• Move an object rest
• Change the shape, size of anobject
• Stop the moving object.
Concept
Map
Type
s
Friction
Muscular
Gravitationa
l
Magnetic
Electrostatic

16. 4) Galileo’sexperiment of motion of an object on an
inclined plane:-
h h
When a marble rolls down an inclined plane, its velocity increases and when it
goes up on the second inclined plane, its velocity decreases. If the inclinations
of both the planes are equal, then the marble will reach the same height which it
rolled down. If the inclination of the second plane is decreased, it will travel
more distance to reach the original height. If the inclination of the second plane
is made horizontal, the marble will travel forever trying to reach the same
height. An unbalanced force is required to change the motion of the marble but
no force is needed to sustain the uniform motion of the marble.
https://www.youtube.com/watch?v=b1jU9aJowW0

17. 5) NEWTON’SLAWS OF MOTION:-
Newton’s first law of motion states that :- ‘An object
remains in a state of rest or in uniform motion in a straight
line unless compelled to change that state by an applied
force.’
Inertia :- The natural tendency of objects to remain in a
state of rest or in uniform motion is called inertia.
This is why the first law of motion is also known as the
law of inertia.
Click for video
https://www.youtube.com/watch?v=YAVgfWoay6I

19. 90 DEGREE IN A RIGHT
ANGLE 26 LETTERS OF
THE ALPHABET 7 DAYS
OF THE WEEK
7 WONDERS OF THE
WORLD 12 SIGNS OF
ZODIAC

20. 6) I NERTIAAND M
ASS:-
A body at rest continues to be at rest and a body in
motion continues to be in motion. This property of a body
is called its inertia.
The inertia of a body is measured by the magnitude of
force required to change the state of the body. The force
required to change the state of a heavier body is more
than the force required to change the state of the lighter
body. This is because the mass of the heavier body is
more than the mass of the lighter body.
So ‘The mass of a body is a measure of its inertia.’

21. Click for video
https://www.youtube.com/watch?v=IiHccDhLSiE

23. (a) Threetimes
(c) Five times
(b) Four times
(d) Six times
Type of inertia that tends to resist the change in case of an “Athlete often jumps before taking a long jump “
(a) Inertia ofdirection
(c) Uniformly accelerated motion
(b) Inertia of motion
(d) Inertia ofrest
Inertia is a force which keeps stationaryobjects at rest and moving objects in motion at constant velocity.
TRUE or FALSE
1. In the following example, try to identify the number of times the velocity of ball changes:
“A football player kicks a football to another player of his team who kicks the football towards the goal.
The goalkeeper of the opposite team collects the football and kicks it towards a player of his ownteam.”
2.
3.
LETS POLL!!!!

24. EXAMPLESOF
INERTIA :-
i)If a striker hits a pile of coins on a carrom board, the lowest coin
moves out and due to inertia of rest, the other coins fall down.
ii)If a coin placed on a playing card over a tumbler is flicked with the
finger, due to inertia of rest, the coin falls down into the tumbler.
iii)When we travel in a car and the driver applies the brakes suddenly,
we tend to fall forward due to inertia of motion.
Person sitting in a car falls backwards,
when the car suddenlystarts.
inertia ofrest
When a moving car suddenly stopsthe
person sitting in the car falls forward
An athlete runs a certain distance before
taking a longjump
When we shake the branch of a tree, the
leave or the fruits fallsdown
When a car moves round a curve the
person sitting inside is thrown outwards

25. IN-
TEX
T
QUE
STIO
NS
PAG
E
1. Which of the following has more inertia:
(a) a rubber ball and a stone of the same size?
(b) a bicycle and a train?
(c) a five-rupees coin and a one-rupeecoin?
Mass is a measure of the inertia of a body. The greater the mass of a body; the greater is its inertia.
(a) Since, M(stone) > M(rubber ball). Hence, Inertia(stone) > Inertia (rubber ball).
(b) Since, M(train) > M(bicycle). Hence, Inertia (train) >Inertia(bicycle).
(c) Since, M(five rupee) > M(one-rupee). Hence, Inertia(five rupee) >Inertia(one-rupee).
Concept Insight: More mass means more inertia.
2. In the following example, try to identify the number of times the velocity of the ball changes. “A football player kicks a football to another player of
his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own
team”. Also identify the agent supplying the force in each case.
Agent supplyingthe force Change invelocity ofball
1. First playerkicks afootball. Velocity from ‘O’ changes to ‘u’
2.Second player kicks the footballtowards thegoal. Velocity changes again
3.The goalkeeper collects thefootball. Velocity becomes O
4.Goalkeeper kicks it towards aplayer Of histeam Change invelocity takesplace

26. IN-TEXT
QUESTI
ONS
(CONTIN
UE..)
PAGE
118
3. Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.
When the tree's branch is shaken vigorously the branch attain motion but the leaves stay at rest.
Due to the inertia of rest, the leaves tend to remain in its position and hence detaches from the
tree to fall down.
4. Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?
When a moving bus brakes to a stop: When the bus is moving, our body is also in motion, but due to sudden brakes, the
lower part of our body comes to rest as soon as the bus stops. But the upper part of our body continues to be in motion and
hence we fall in forward direction due to inertia ofmotion
When the bus accelerates from rest we fall backwards: When the bus is stationary our body is at rest but when the bus
accelerates, the lower part of our body being in contact with the floor of the bus comes in motion, but the upper part of our
body remains at rest due to inertia of rest. Hence we fall in backward direction.
5. The mud particles sticking on the rim of a bicycle wheel leave the rim of the wheel tangentially when it startsmoving.
Explain.
This happens because of inertia of direction. When the bicycle wheel rotates, centripetal force is not exertedon the mud
particles, so mud particles because of inertia of direction continue to move in straight line tangential to the wheel

27. NCERT EXCERCISE
Page 128
2. When a carpet is beaten with a stick, dust comes out of it. Explain.
When the carpet is beaten, it is suddenly set into motion. The dust particles tend to remain
at rest due to inertia of rest, therefore the dust comes out of it.
3. Why is it advised to tie any luggage kept on the roof of a bus with a rope?
When a bus starts suddenly, the lower part of the luggage kept on the roof being in contact with the bus begins to move
forward with the speed of bus, but the upper part tends to remain at rest due to inertia of rest. Therefore, the upper part
is left behind and hence luggage falls backward. So, it is advised to tie any luggage kept on the roof of a bus with a
rope.

28. Concept
Map
NEWTON’S FIRST LAW OF
MOTION
LawofInertia
QualitativeLawof force
A body remains in the state of rest or
uniform motion in a straight line unless and
until an external unbalanced force acts on it.
Inertia
Inertiaof rest
Inertiaof motion
Inertiaof direction
Also called
Statement
Inertia is the natural tendency
of an object to resist a change
in its state of motion or of rest.
More mass=more inertia Lessmass=Less inertia
Types

29. https://www.youtube.com/watch?v=ihwcw_ofuME
Meditation
PERIOD -
3

30. Click for video
https://www.youtube.com/watch?v=0zxTIn67q3Y

34. 1. Acar and a truck have same momentum. Whose velocity is more?
A. Car B. Truck
2. How the momentum of an object changes when mass of an object is doubled.
A. Remains same B. four times C. double
LETS POLL!!!!

39. What will be the momentum of a stone having mass of 10 kg when it is thrown with a velocity of 2m/s?
Solution: Given,
Mass (m) = 10kg
Velocity (v) =2m/s
Momentum (p) =?
We know that, Momentum (p) = Mass (m) × Velocity (v)
Therefore, p=10 × 2
=20kgm/s
p=20kgm/s
Thus the momentum of the stone =20kgm/s
Howmuchmomentumwillanobjectofmass10kgtransfertothefloorif it fallsfromaheightof5m?(g=
10m/s2)
s =
5m,a =
g=10m/s2,u=0,v=?
V2 - u2 = 2as ⟹ v2
=u2
+2as
v2=
0+
2X10X5=
100
v
=10m/s
Momentum of object
p =
mv
=
10 × 10 = 100kgm/s
PRACTICE
NUMERICAL

40. Answer
Mass of the dumbbell (m) = 10 kg
Distance covered by the dumbbell (s) = 80 cm = 0.8 m
Acceleration in the downward direction (a) = 10 m/s2
Initial velocity of the dumbbell (u) =0
Final velocity of the dumbbell (when it was about to hit the floor) = v
According to the third equation ofmotion:
v2 = u2 +2as
v2 = 0 + 2 (10)0.8
v = 4 m/s
Hence, the momentum with which the dumbbell hits the floor is
= mv = 10 × 4 = 40 kg m s−1
NCERT EXCERCISE
Page 129
18. How much momentum will a dumbbell of mass 10 kg transfer to the floor if it falls from a height of 80 cm?
Take its downward acceleration to be 10 m s−2.

41. RECAP

42. 8) Newton’s secondlawof motion :-
Newton’s second law of motion states that :- ‘ The rate of change of
momentum of an object is proportional to the applied force in the
direction of force.’
Click for video
https://www.youtube.com/watch?v=FNIetgoLPHQ

44. As, F = ma
⟹
One Newton is defined as the force that is required to accelerate a mass
of 1kg by 1m.s-2 in the direction of appliedforce.
DEFINITION OF 1NEWTON

45. Guess The Body Parts
1. A Thing That A CarpenterUse
2. Something That A Shoe Has
3. Name Of AnAirlines
4. Excess Of Anything
5. Symbol OfLove
6. Defence People Base Known As
7. An Animal Like Rabbit Which Runs Fast
8. An Evergreen Tree Of Warm Region
9. One Side Of A Coin
10. Looks Like Walnut
11. Something That A Table Has
12. What Do U Call Yourself
Example: 1.Nail

46. 1.Nail
2.Soul
3.Palm
4.Abdomen
5.Heart
6.Navel
7.Hair
8.Lip (Eucalyptus)
9.Head
10. Brain
11. Leg
12. Eye

47. impulse
APPLICATION OF IMPULSEINEVERYDAY LIFE

48. A KARATE
MASTER
CAN BREAK
A PILE OF?
because he strikes it very fast and in
the process produces a large
momentum of his hand which is
reduced to zero in a very short time
when his hand strikes the tiles. this
exerts a large force on the pile of tiles
thus breaking it.

49. Calculate the force needed to speed up a car with a rate of 5ms–2, if the mass of the car is 1000 kg.
A. 500 N B. 5000 kg C. 5000 N D. 50 kg
To accelerate an object to a rate of 2m/s2, 10 N force is required. Find the mass of object.
A. 5 kg B. 20 kg C. 12 kg D. 0.5 kg
What the acceleration a vehicle having 1000 kg of mass will get after applying a force of 5000N?
A. 50ms−2 B. 5 ms−2 C. 500ms−2 D. 1ms−2
LETS POLL!!!!

50. Initial velocity, u = 0
Distance travelled, s =400 m
Time taken, t = 20s
We know from third equation of motion with uniform
acceleration
or, 400 = 0 + ½ a (20)2
or, a = 2 m/s2
Now, m = 7 metric tonnes = 7000kg,
a = 2 m/s2
Or, F = ma = 7000 × 2 = 14000 N
6.A stone of 1 kg is thrown with a velocity of 20 m s−1 across the frozen surface of a lake and comes to rest after
travelling a distance of 50 m. What is the force of friction between the stone and the ice?
Initial velocity of the stone, u= 20 m/s
Final velocity of the stone, v= 0
Distance covered by the stone, s= 50m
Now from 2nd equation of motion of uniform acceleration
v2 = u2 +2as
Or, 0 - 202 = 2a × 50,
Or, a = – 4 ms-2
So Force of friction, F = ma = – 4N
NCERT EXCERCISE
Page 128
5.A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its
acceleration. Find the force acting on it if its mass is 7 metric tonnes (Hint: 1 metric tonne = 1000 kg).
Given from question s = ut + ½ at2

51. Newton's second law of motion states that rate of change of momentum of an object is directly proportional to the applied
force and takes place in the direction in which the force acts.
If there is no force acting on the body, the equation (1) can be written as,
→ v = u ... (2)
This means initial velocity is equal to final velocity when no force acts on the body.
Thus, equation (2) represents Newton's first law of motion.
Newton's first law of motion states that a body at rest will remain at rest and body in motion will remain in
motion in straight line with a uniform speed, unless an external force acts on it.
DERIVE NEWTON’S FIRST LAW OF MOTION FROM
SECOND LAW OF MOTION

52. You have 2 buckets
of water, inside the
1st bucket the
temperature of the
water is 25ºC, inside
the 2nd bucket the
water is 25ºF. You
drop a coin into each
bucket from the
same height and they
hit water at exactly
the same time.

53. THE COIN INTHE 1ST BUCKET.
AT 25ºC WATER ISLIQUID,WHILEAT 25ºF ITTURNS INTO
ICE.

54. 7.A 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force
of 40000 N and the track offers a friction force of 5000 N, thencalculate:
(a) the net acceleratingforce;
(b)the acceleration of the train; and
(c)the force of wagon 1 on wagon 2.
(a) Force exerted by the engine, F = 40000 N
Frictional force offered by the track, Ff = 5000 N
Net accelerating force, Fa = F − Ff = 40000 − 5000 = 35000N
Hence, the net accelerating force is 35000N.
(b) Acceleration of the train= a
The engine exerts a force of 40000 N on allthe five wagons.
Net accelerating force on the wagons, Fa = 35000 N
Mass of the wagons, m = Mass of a wagon x Number ofwagons
Mass of a wagon = 2000kg
Number of wagons = 5
∴ m = 2000 × 5 = 10000kg
Mass of engine (m’)=8000kg
Total mass, M = m + m’ = 10000 +8000=18000kg
From Newton’s second law ofmotion
Fa= Ma
a=F/m = 35000 /18000 = 1.944 m/s2
(c) Mass of all the wagons except wagon 1is
4 × 2000 = 8000kg
Acceleration of the wagons = 1.944 m/s2
Thus,
force exerted on all the wagons except wagon 1
= 8000 × 1.944 = 15552 N
Therefore, the force exerted by wagon 1 onthe
remaining four wagons is 15552N

55. 8.An automobile vehicle has a mass of 1500 kg. What must be the force between the vehicle and road if the vehicle is
to be stopped with a negative acceleration of 1.7 m /s2?
Answer
Given in the question
ass of the automobile vehicle (m)= 1500kg
Final velocity(v)= 0 (finally the automobilestops)
Acceleration of the automobile(a) = −1.7 m/s2
From Newton’s second law ofmotion
Force = ma = 1500 x (−1.7) = −2550N
Hence, the force between the automobile and the road is −2550 N, in the direction opposite to the motion of the automobile.

56. If the mass of a body and the force acting on it are both doubled, what
happens to the acceleration?
A. Will remain same
B. becomes double
C. Becomes four times
D. Become one fourth times
LETS POLL!!!!

57. Concept
Map
SECOND LAW OF
MOTION
Quantitative Lawofforce
Statement
Momentum
p = mv
S.Iunit:kgm/s Vector p∝𝑚𝑎𝑠𝑠
p∝velocity
The rate of change of
momentum of an object is
proportional to theapplied
unbalanced force in the
direction of theforce.
Formula
F = ma
S.Iunit:
Newton (N)
Vector
One Newton is defined as the
force that is required to
accelerate a mass of 1kg by
1m.s-2 in the direction of applied
force.
Produces
acceleration
inthe body

58. 10) NEWTON’STHIRD LAW OF
MOTION:-
Newton’s third law of motion states that :- ‘To every action there is
an equal and opposite reaction and they act on two different bodies.’
To prove that action and reaction are equal and opposite :-
Take two spring balances A and B connected together. Fix the spring
balance B to a rigid support. When a force is applied by pulling the free
end of the spring balance A, both the spring balances show the same
readings. This shows that the force exerted by the spring balance A on
B is equal but opposite in direction to the force exerted by spring
balance B on A . The force exerted by the spring balance A on B is
action and the force exerted by the spring balance B on A is reaction.
A
B
Click for video
Click for video
https://www.youtube.com/watch?v=c5ZgAxcjqQo
https://www.youtube.com/watch?v=BlgPnnwUNOQ

59. EXAMPLESOF ACTIONAND
REACTION :-
i) When a bullet is fired from a gun, it exerts a forward force (action) on
the bullet and the bullet exerts an equal and opposite force on the gun
(reaction) and the gun recoils.
Recoil force
on the gun
Accelerating force
on the bullet
Action
Reaction
ii) When a sailor jumps out of a boat, he exerts a backward force of the
boat (action) and the boat exerts an equal and opposite force on the
sailor (reaction) and the sailor jumps forward.
Click for video
https://www.youtube.com/watch?v=uI-eFzkBeHg

60. There are 2 cars, the blue car is going 60mph and the red car is going 40mph. They
both started at the same time however they still cross each other at some point.
Question. How is that possible?

61. THEY ARE TRAVELLING INOPPOSITE
DIRECTIONS.

62. Move one cup to get this order.

65. The action and reaction forces referred to in the third law
(A) May act on different objects
(B) Must act on different objects
(C) Must act on the same object
(D) Need not be equal in magnitude but act in the same direction
LETS POLL!!!!

66. IN-
TEXT
QUE
STIO
NS
PAG
1. If action is always equal to the reaction, explain how a horse can pull a, cart?
Ans. The third law of motion states that action is always equal to the reaction but they act on two different bodies.
In this case the horse exerts a force on the ground with its feet while walking, the ground exerts an equal andopposite
force on the feet of the horse, which enables the horse to move forward and the cart is pulled by thehorse.
2. Explain, why is it difficult for a fireman to hold a hose, which ejects a large amount of water at a high velocity.
Ans. The water that is ejected out from the hose in the forward direction comes out with a large momentum and equal
amount of momentum is developed in the hose in the opposite direction and hence the hose is pushed backward. It
becomes difficult for a fireman to hold a hose which experiences this large momentum.

67. The logic is that Action and Reaction always act on different bodies, so they cannot cancel each other. When we
push a massive truck, the force of friction between its tyres and the road is very large and so the truck does not move.
The force of friction cancel the force applied by person push. So student justification is correct
NCERT EXCERCISE
Page 129
12. According to the third law of motion when we push on an object, the object pushes back on us with an equal and
opposite force. If the object is a massive truck parked along the roadside, it will probably not move. A student justifies this
by answering that the two opposite and equal forces cancel each other. Comment on this logic and explain why the truck
does not move.

68. 11) CONSERVATION OF
MOMENTUM :-
•‘The sum of momenta of two objects before collision is equal to the sum of momenta
after collision provided there is no unbalanced forces acting on them.’
• This means that the total momentum of the two objects is unchanged or conserved by
collision.
The Law of conservation of momemtum states that :-
uA uB vA vB
FBA FAB
A B A B
mA
A
mB
B
mA mB
Click for video
https://www.youtube.com/watch?v=3WX7bweJK-k

71. Stretch
it out
S T E P -1 S T E P -2
S T E P -3 S T E P -4

72. SIGN
CONVENT
ION

74. A. 0m/s B.8 m/s C. 4m/s D. 16m/s
LETS POLL !!!!

75. The system of gun and bullet
APPLICATIONS OF CONSERVATION
OF MOMENTUM
Before Firing After Firing
Momentum of bullet =0
Momentum of gun = 0
Total momentum of the system =0
Momentum of bullet =
Momentum of gun = MV
Total momentum of the system=
According to the law of conservation of momentum, momentum before collision and after collision must be
same.
Negative sign indicates that direction of motion of gun is in opposite
direction.

77. Why does a gunman get a jerk on firing a bullet?
Gunman gets a jerk on firing a bullet because when a bullet is fired from a gun, the force
sending the bullet forward is equal to the force sending the gun backwards but due to high
mass of the gun, it moves only a little distance backwards giving a jerk to the gunman.

79. ifyouputball 9upsidedowninthehole
placeballs 11and13intoothertwoholes
6 11 13

80. Rocket and Jet Plane
Fuel and oxygen is burnt in the ignition chamber. As hot
gases escape from a rear opening, with some momentum,
the rocket moves in the forward direction with the same
momentum.
A man Jumping from a Boat
When a man jumps from the boat to the shore, the boat
is pushed backward.

82. What is the total momentum of bullet and the gun before firing?
A. Depends on size ofgun
B. depends on size ofbullet
C. zero
LETS POLL!!!!

83. 3. From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m/s. Calculate the initial recoil
velocity of the rifle.
Ans. Given Data,
(m1) Mass of rifle = 4 kg
(m2) Mass of bullet = 50 g = 0.05 kg
(v2) Velocity of bullet = 35 m/s
(v1) Recoil velocity of rifle = ?
According to the law of conservation of momentum
Momentum of rifle = momentum ofbullet
m1u1 + m2u2= m1v1+ m2v2
⇒ 4×0 + 0.05×0 = 4×v1 +0.05×35
⇒ 0 = 4×v1+1.75
⇒ −4×v1=1.75
⇒ v1 = 1.75−4 = −0.4375 ≈−0.44m/s
Here negative sign of velocity of rifle shows that rifle moves in
the opposite direction of the movement of bullet. Therefore, recoil
velocity of rifle is equal to 0.44m/s
4 Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 m/s and 1 m/s,
respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m/s. Determine the velocity of the
second object.
Given, m1u1 + m2u2 = m1v1 + m2v2
(m1) Mass of first object = 100 g = 0.1kg ⇒0.1×2 + 0.2×1 = 0.1 ×1.67 + 0.2 × v2
(u1) Initial velocity of first object = 2 m/s ⇒0.2 + 0.2. =. 0.167 × 0.2 × v2
(v1) Final velocity of first object after collision = 1.67 m/s ⇒0.4 − 0.167 = 0.2 ×v2
(m2) Mass of second object = 200 g = 0.2 kg ⇒v2 =0.233/0.2=1.165ms−1
(u2) Initial velocity of second object = 1 m/s Thus, velocity of the second object after collision = 1.165 ms−1
(v2) Final velocity of second object after collision =?
IN-
TEXT
QUE
STIO
NS
PAG

84. Mass of one of the objects (m1 )= 1.5 kg
Mass of the other object ( m2 )= 1.5 kg
Velocity of m1 before collision (u1 )= 2.5 m/s
Velocity of m2, moving in opposite direction before collision (u2 )= −2.5m/s
(- sign denotes this is in opposite direction)
Let v be the velocity of the combined object after collision
By the law of conservation ofmomentum
Total momentum after collision = Total momentum before
collision,
(m1 + m2) v = m1u1 + m2u2
(1.5 + 1.5) v = 1.5 × 2.5 +1.5 × (–2.5)
Or, v = 0 m/s
So They come to rest aftercollision
NCERT EXCERCISE
Page 128
11. Two objects, each of mass 1.5 kg are moving in the same straight line but in opposite directions. The velocity of each
object is 2.5 m/s before the collision during which they stick together. What will be the velocity of the combined object after
collision?

85. NCERT EXCERCISE
Page 129
13.A hockey ball of mass 200 g travelling at 10 m/s is struck by a hockey stick so as to return it along its original path
with a velocity at 5 m /s. Calculate the change of momentum occurred in the motion of the hockey ball by the force
applied by the hockeystick.
Answer
Given in the question
Mass of the hockey ball (m) = 200 g = 0.2 kg
Hockey ball travels with velocity ( v1 )= 10 m/s
Initial momentum = mv1
Hockey ball travels in the opposite direction with velocity(v2 ) = −5 m/s
Final momentum = mv2
Change in momentum = mv1 − mv2 = 0.2 [10 − (−5)] = 0.2 (15) = 3 kgm/s
Hence, the change in momentum of the hockey ball is 3kgm/s

86. Find the odd

88. Find the odd

90. Answer
Given in the question
Initial velocity (u )= 150m/s
Final velocity(v) = 0 as since the bullet finally comes to rest
Time taken to come to rest( t)= 0.03 s
According to the first equation of motion withuniform
acceleration
v= u + at
Acceleration of the bullet(a)
0 = 150 + (a × 0.03s)
a = -150 / 0.03 = -5000m/s2
(Negative sign indicates that the velocity of the bullet is
decreasing.)
According to the third equation of motion ofuniform
acceleration
v2= u2+ 2as
0 = (150)2+ 2 (-5000)
= 22500 / 10000
= 2.25 m
Hence, the distance of penetration of the bullet into the block is
2.25 m.
From Newton’s second law of motion:
Force, F = Mass ×Acceleration
ass of the bullet, m = 10 g = 0.01 kg
Acceleration of the bullet, a = 5000m/s2
F = ma = 0.01 × 5000 = 50N
Hence, the magnitude of force exerted by the wooden blockon
the bullet is 50 N.
14 . A bullet of mass 10 g travelling horizontally with a velocity of 150 m s−1 strikes a stationary wooden block and
comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block.Also calculate the magnitude
of the force exerted by the wooden block on the bullet.

91. 15.AN OBJECT OF MASS 1 KG TRAVELLING IN A STRAIGHT LINE WITH A VELOCITY OF 10 M S−1
COLLIDES WITH, AND STICKS TO, A STATIONARYWOODEN BLOCK OF MASS 5 KG. THEN
THEY BOTH MOVE OFF TOGETHER IN THE SAME STRAIGHT LINE. CALCULATE THE
TOTAL MOMENTUM JUST BEFORE THE IMPACT AND JUST AFTER THE IMPACT.ALSO,
CALCULATE THE VELOCITY OF THE COMBINED OBJECT.
Answer
Mass of the object (m1 )= 1 kg
Velocity of the object before collision( v1 )= 10 m/s
Mass of the stationary wooden block (m2 )= 5 kg
Velocity of the wooden block before collision( v2 )= 0 m/s
Total momentum before collision = m1 v1 + m2 v2
= 1 (10) + 5 (0) = 10 kg m s−1
It is given that after collision, the object and thewooden
block stick together.
Total mass of the combined system = m1 + m2
Velocity of the combined object = v
According to the law of conservation of momentum:
Total momentum before collision = Total momentum after
collision
m1 v1 + m2 v2 = (m1 + m2) v
1 (10) + 5 (0) = (1 + 5) v
v = 10 / 6
= 5 / 3
The total momentum after collision is also 10 kg m/s.
Total momentum just before the impact = 10 kg m /s
Total momentum just after the impact = (m1 + m2) v = 6 × 5 /3
= 10 kg ms-1
Hence, velocity of the combined object after collision
= 5 / 3 ms-1

92. 16.An object of mass 100 kg is accelerated uniformly from a velocity of 5 m/s to 8 m/s in 6 s. Calculate the initial and
final momentum of the object.Also, find the magnitude of the force exerted on the object.
Answer
Initial velocity of the object (u) = 5 m/s
Final velocity of the object (v) = 8 m/s
ass of the object (m) = 100kg
Time take by the object to accelerate, t = 6 s
Initial momentum = mu = 100 × 5 = 500 kg m/s
Final momentum = mv = 100 × 8 = 800 kg m/s
Force exerted on the object, F =Change in momentum/Time taken
= (mv – mu) / t
= m (v-u) / t
= 800 - 500
= 300 /6
= 50 N
Initial momentum of the object is 500 kg m/s
Final momentum of the object is 800 kg m /s
Force exerted on the object is 50N.

93. Concept
Map
NEWTON’S THIRD LAW OF
MOTION
Statement
follows
Law of conservation of energy
For every action there is a
equal and opposite reaction
Total momentum before
collision is equal to the
total momentum after
collision.
   

   

  
 
  
- ve velocity ⟹oppositedirection
Recoil of Gun

94. FORCE & LAWS OF MOTION
Balanced and unbalanced
force
Newton’s 1st law ofmotion
Newton’s 2nd law of motion
Newton’s 3rd law ofmotion
Conservation of momentum
Inertia of rest:
1.Fruits fall down due to inertia of
rest when the branches of a tree are
shaken.
2. Dust particles on a carpet fallif
we beat the carpet with a stick.
Inertia of motion:
1. A person trying to get down
from a running bus falls forward
2.The swirling of milk in a glass
continues even after the stirring
is stopped
Momentum:p=mv
Mathematical
expression:
F=ma
SI unit of force: Newton or
kg m/s2
Application:
1. A karate player breaks the piles of
tiles or bricks with a single blow
2. A cricket player lowers hishands
while catching the ball.
FAB = -FBA
Every action has an equal
& opposite reaction – acts
on two different objects.
Application:
1.Walking: While walking we push ground
backwards, as a result the ground push us
forward.
2. During the rowing of a boat, the boatman
pushes the water backwards with the rows
Mathematical expression:
mAuA + mBuB = mAvA +
mBvB
M
I
N
D
M
A
P Inertia & mass:
More the mass
more is its inertia