## Chapter 3 - Laws of Motion Exercise 113

Question 1
What do you mean by inertia of motion?
Solution 1
The property by which a body neither changes its present state of rest or of uniform motion in a straight line nor tends to change the present state,is known as inertia.
Question 2
When a sports car and a loaded van are travelling at a speed of 50 km/h, which vehicle requires more force to stop?
Solution 2
As mass of loaded van is greater than sports car so it would require more force to stop.

Question 3
What is the acceleration produced by a force of 12 N exerted on an object of mass 4 kg?
Solution 3
We know force = mass X acceleration.
a= f/m = 12 N / 4 kg. = 3 ms-2
so acceleration of the body would be 3 ms-2.
Question 4
What is the ratio of SI to CGs units of force?
Solution 4
SI unit of force is Newton whereas CGS unit of force is dyne.
1 newton / 1dyne = 105.

Question 5
Write the SI unit of momentum.
Solution 5
SI unit of momentum is kgms-1.
Question 6
Define momentum of a body.
Solution 6
Momentum is defined as the amount of motion contained in the body. It is given by the product of the mass of the body and its velocity.

Question 7
Name the physical quantity associated with the motion of a body.
Solution 7
Momentum is the physical quantity associated with the motion of the body.
Question 8
Momentum is possessed by bodies in ---------------
Solution 8
Momentum is possessed by bodies in MOTION.

Question 9
Which has more momentum: a fast pitched soft ball or a soft pitched soft ball?
Solution 9
A fast pitched soft ball has more momentum.
Question 10
What is the ratio of SI units to CGS units of momentum?
Solution 10
SI unit of momentum is kgms-1 and CGS unit of momentum is g cms-1.
And their ratio is = 1000 X 100 g ms-1= 1:10.

Question 11
What will be the momentum of a body at rest?
Solution 11
A body at rest has zero momentum as its velocity is zero.
Question 12
Give one example each of inertia of rest and inertia of motion.
Solution 12
A book lying on a table will remain placed at table unless it is displaced by some external force. This is an example of inertia of rest.
A ball rolling on the ground  will continue to roll unless the external force , the force of friction between the ball and the ground stops it.

Question 13
State Newton's third law of motion.
Solution 13
According to Newton's third law, for every action there is always an equal and opposite reaction.
Question 14
What do you mean by action?
Solution 14
When a force acts on a body then this is called an action.

Question 15
Do action and reaction act on the same body?
Solution 15
No, action and reaction never act on a same body they always act simultaneously on two different bodies.
Question 16
Name the law of motion which gives the definition of force.
Solution 16
2nd law of motion gives the definition of force.

Question 17
A boy jumps to a dock from a boat. The boat moves away from the dock. Which law explains the statement?
Solution 17
Newton's third law explains this statement.
Question 18
Is force a scalar or a vector quantity?
Solution 18
Force is a vector quantity.

Question 19
If a number of forces act on a stationary body at the same point, then what do you conclude from it?
Solution 19
This means these forces are balanced forces.
Question 20
Why do passengers tend to fall sideways when the bus takes a sharp turn?
Solution 20
Passengers tend to fall sideways when the bus takes a sharp turn due to the inertiaof direction.

Question 21
Why are passengers thrown in the forward direction when a running bus stops suddenly?
Solution 21
Passengers are thrown in the forward direction as the  running bus stops suddenly because due to their inertia of motion, their upper body continues to be in the state of motion even though the lowerbody comes to rest when the bus stops.
Question 22
Why do passengers tend to fall backward when it starts suddenly?
Solution 22
Passengers tends to fall in backward direction when bus starts suddenly because due to their inertia of rest, as soon as the bus starts, their lower body comes in motion but the upper body continues to be in the state of rest.

Question 23
The greater is the -------- the greater is the inertia of an object.
Solution 23
The greater is the MASS , the greater is the inertia of the object.
Question 24
Can internal forces change the velocity of a body?
Solution 24
No, internal forces cannot change the velocity of a body.

Question 25
Why do the dust particles come out of a hanging carpet when it is beaten with a stick?
Solution 25
When a hanging carpet is beaten using a stick, the dust particles will start coming out of the carpet because the part of the carpet where the stick strikes, immediately comes in motion while the dust particle sticking to the carpet remains at rest . Hence a part of the carpet moves ahead alongwith the stick, and the dust particles fall down due to the earth's pull.
Question 26
Why is a tree shaken to get its fruit down?
Solution 26
When we shake the branches of a tree, the fruits and leaves remain in state of rest while branches comes in rest so fruits and leaves are detached from the tree.

Question 27
Which would require a greater force: accelerating a 10 g mass at 5 ms-2, or accelerating a 20 g mass of 2 ms-2?
Solution 27
We know force = mass X acceleration
F1 = 10 X 5 = 50 dyne.
F2 = 20 X 2 = 40 dyne.
So first body require more force.
Question 28
Solution 28

Question 29
Name the different kinds of inertia an object can possess. Give an example of each.
Solution 29
An object possess two kind of inertia, inertia of rest and inertia of motion.A book lying on a table will remain placed at table unless it is displaced by some external force. This is an example of inertia of rest.
A ball rolling on the ground  will continue to roll unless the external force , the force of friction between the ball and the ground stops it.
Question 30
Define one Newton. How much maximum acceleration can it produce in a mass of 1 kg?
Solution 30
1 Newton is the force which when applied to a body of unit mass   produces a unit acceleration in it. 1 newton would produce acceleration of   1 ms-2 in a mass of 1 kg.

Question 31
The acceleration produced by a force in an object is directly proportional to the applied ------------ And inversely proportional to the ----------- Of the object.
Solution 31
The acceleration produced bya force in an object is directly proportional to the applied FORCE and inversely proportional to the MASS of the object.
Question 32
What is the SI unit of force?
Solution 32
SI unit of force is Newton (N).

Question 33
Name the physical quantity associated with N kg-1.
Solution 33
Acceleration is the physical quantity associated with N kg-1.
Question 34
Solution 34
1 N = 105 Dyne.

## Chapter 3 - Laws of Motion Exercise 114

Question 1
An object undergoes an acceleration of 8 ms-2 starting from rest. Find the distance travelled in 5 seconds.
Solution 1
initial velocity of the object = 0 ms-1
Acceleration of the object = 8 ms-2.
Time = 5 s.
Distance covered would be S = ut + 1/2 at2.
S = 1/2 X 8 X 5 X5 = 100 m.
Question 2
A truck rolls down a hill with constant acceleration after starting from rest. It travels a distance of 100 m in 10 s. find its acceleration. Find the force acting on it, if its mass is 5 metric tons. (tonne)
Solution 2
Initial velocity of the truck = 0 ms-1
Distance covered by truck = 100 m
Time taken to cover this distance = 10 s.
We know Distance covered would be S = ut + 1/2 at2.
100 =1/2 Xa X100
a= 2 ms-2.
Mass of truck = 5 metric tons = 5000 kg.
Force acted on truck = mass X acceleration
Force = 5000 X 2 = 10000 N.

Question 3
Name the physical entity used for quantifying the motion of a body.
Solution 3
Momentum is used for quantifying the motion of body.
Question 4
Why do you feel a backward jerk on your shoulder when you fire a gun?
Solution 4
When we fire a gun, a force is exerted in the forward in the forward direction as the bullets comes out; in reaction to which an equal and opposite force is act in the backward direction and hence, we feel a backward jerk on the shoulder.

Question 5
How does a person move forward during swimming?
Solution 5
A person applies force on water in backward direction and water according to third law of motion water apply an equal and opposite force in forward direction which helps a person to swim.
Question 6
Name the principle involved in the working of a jet engine.
Solution 6
Newton's third law of motion is involved in the working of a jet plane.

Question 7
Is the statement correct?
A rocket can propel itself in vacuum.
Solution 7
Yes, a rocket can propel itself in a vacuum once it is given initial velocity.
Question 8
Since action and reaction forces are always equal in magnitude and opposite in direction, how can anything be ever accelerated?
Solution 8
Action is equal and opposite to reaction but they act on different bodies and object moves as movement requires an unbalanced force and these are provided once inertia is overcome.

## Chapter 3 - Laws of Motion Exercise 125

Question 1
Who stated the law of gravitation?
Solution 1
Sir Isaac Newton stated the law of gravitation.
Question 2
The force of attraction between any two material objects is called --------------.
Solution 2
The force of attraction between any two material objects is called FORCE OF GRAVITATION.

Question 3
The gravitational force of the earth is called earth's---------.
Solution 3
The gravitational force of the earth is called earth's  GRAVITY.
Question 4
The gravity is a particular case of -----------.
Solution 4
The Gravity  is a particular case of GRAVITATIONAL FORCE OF EARTH.

Question 5
The value of G is extremely --------- (Small/large/infinite)
Solution 5
The  value of G is extremely  SMALL.
Question 6
Is the law of gravitation applicable in case of the sun and the moon?
Solution 6
Yes the law of gravitation is also applicable in case of the sun and moon.

Question 7
Solution 7
we know that law of gravitation.
F =  G ( m1Xm2)/R2.
Mass of earth = 6X1024kg.
Mass of the person = 100 kg.
G = 6.7 X10-11 Nm2kg-2.
Radius of earth = 6.4 X 1014.
F =  (6.7 X10-11X 100 X 6 X1014 )/ (6.4 X6.4 X1012) = 981.4N
Force of gravity due to earth acting on a 100 kg person is 981.4 N.
Question 8
Why do objects fall towards the earth?
Solution 8
Objects fall towards the earth due to force of gravitation.

Question 9
Why don't you feel the force of attraction between your friend sitting close to you and yourself?
Solution 9
Because the masses of persons are not large enough to overcome the value of small constant of gravitation so the force of gravitation is very small and negligible to feel.
Question 10
A ball is thrown up with a speed of 4.9 ms-1.
(a) Calculate the maximum height it would gain before it begins to fall.
(b) Also, calculate the time it takes to reach this height.
(c) Prove that the time of ascent is equal to the time of descent.
Solution 10
Initial speed of ball is = 4.9 ms-1.
Acceleration due to gravity = -9.8 ms-2.
(a) We know v2 - u2 =2as
At highest point final velocity is zero so
0 - 4.9 X 4.9 = 2 X (-9.8) S
S = 1.125 m
(b) We know v = u + at
0 = 4.9 - 9.8 t
T = 0.5 sec.
(c) for highest point initial velocity is zero
Acceleration due to gravity is = 9.8 ms-2.
Final velocity at ground is v
V2 - 0 = 2 X9.8 X 1.125
V = 4.9 ms-1.
Time taken to reach ground from highest point
V = u + at
4.9 = 0 + 9.8 t
T = 4.9/9.8 = 0.5 sec.
So time of ascent is equal to time descent.

Question 11
What is the relation between 'g' and 'G'?
Solution 11
g = GM/R2.
Question 12
State Newton's law of gravitation.
Solution 12
Every object in the universe attracts every other object with a force directly proportional to the product of their masses  and inversely proportional to the square of distance between them.

Question 13
What is the value of g at the surface of the earth?
Solution 13
Value of the g at the surface of the earth is 9.8ms-2.
Question 14
When some rock is brought to the earth from the surface of the moon, Will its mass and weight change?
Solution 14
Mass of the body is constant at all positions so mass will not  change. But weight will change as gravity on the surface of earth is almost 6 times than on the surface of the moon, so its weight will increase almost 6 times on the surface of earth.

Question 15
Where will you weigh more: at the centre of the earth or at the surface of the earth?
Solution 15
We will weigh more on the surface of the earth.
Question 16
Name an instrument used to measure the mass of a body.
Solution 16
Beam balance is used to measure the mass of a body.

Question 17
Name the instrument by which the weight of a body can be measured.
Solution 17
Spring scale is used to measure the weight of a body.
Question 18
Where do you weigh more: at the poles or at equator?
Solution 18
The weight is greater at the poles than the equator.

Question 19
How are kg wt and N related to each other?
Solution 19
Newton 1N  = 9.8 kgwt.
Question 20
Where will you weigh more: at the moon's surface or at the earth's surface?
Solution 20
We will weigh more on earth surface as value of g is greater on earth surface.

Question 21
Does the force of gravitation between two objects depend on the medium between them?
Solution 21
No, the force of gravitation between two objects does not depend on the medium between them.
Question 22
What will happen to the gravitational force of attraction between two objects if the mass of each is doubled and the distance between them is also doubled?
Solution 22
we know that law of gravitation.
F = G ( m1Xm2)/R2.
Now m1 = 2 m1
m2 = 2 m2
R = 2 R
F1 = G ( 2m1 X2 m2)/4R2.
F1 = F
So force between them remains same.

Question 23
Distinguish between gravity and gravitation.
Solution 23
Gravity is the force of attraction between the object and the earth whereas gravitation refers to the force of attraction that exists between any two bodies that possess mass.
Question 24
Define acceleration due to gravity.
Solution 24
Acceleration due to gravity is the acceleration experienced by a body during free fall.

Question 25
Write the relation between g and G.
Solution 25
g = GM/R2.
Question 26
Define the constant of gravitation.
Solution 26
We know that law of gravitation.
F = G ( m1 X m2)/R2.
Here G is universal constant and is called constant of gravitation. It doesnot depend upon on the value of m1,m2 or R.
Its value is same between any two objects in the universe.

Question 27
What are the SI units of constant of gravitation?
Solution 27
SI unit of constant of gravitation is Nm2kg-2.
Question 28
How will the force of gravitation between two objects change if the distance between them is
(a) Halved,
(b) Doubled,
(d) Infinite
(e) Almost zero?
Solution 28
we know that law of gravitation.
F =  G ( m1 X m2)/R2.
(a) If distance between them is halved then put R = R/2.
F = 4 X G( m1 X m2)/ R2.
F1 = 4 F.
(b) If distance between them is doubled then put R = 2R.
F = G( m1 X m2)/ 4R2.
F1 = F/4.
(c) If distance between them is made four times then put R = 4R.
F = G( m1 X m2)/16 R2.
F1 = F/16.
(d) If distance between them is infinite then put R = infinite.
F = G( m1 X m2)/ R2.
F1 = 0.
(e) If distance between them is almost zero then put R = 0.
F = G( m1 X m2)/ 0.
F1 = infinite.

Question 29
All objects in the universe attract each other along the line joining their -------------
Solution 29
All objects in the universe attract each other along the line joining their CENTRES.

## Chapter 3 - Laws of Motion Exercise 126

Question 1
In vacuum, all freely falling objects have the same force. Is it true?
Solution 1
Yes, in absence of gravity all freely falling body have same force acting on them.
Question 2
Solution 2
g= GM/R2
it means acceleration due to gravity is directly proportional to the mass of body and inversely proportional to the square of distance between earth and object.

Question 3
Neglecting air resistance, a body falling freely near the earth's surface has a constant acceleration. (True/False)
Solution 3
Yes a body falling freely near the earth surface has a constant acceleration.
Question 4
At which of the following locations, the value of g is the largest?
(i) On top of the Mount Everest
(ii) On top of Qutub Minar
(iii) At a place on the equator
(iv) A camp site in Antarctica
Solution 4
As we know
g= 1/R2
so value of g is more at poles than equator so value of g is maximum near a camp site in Antarctica as this lie on the pole.

Question 5
At what height above the earth's surface would the value of acceleration due to gravity be half of what it is on the surface? Take the radius of earth to be R.
Solution 5

## Chapter 3 - Laws of Motion Exercise 128

Question 1
What is a force?
Solution 1
Force is that external agency which tends to change the state of rest or the state of motion of a body.
Question 2
A man riding on a car has -----------. Inertia.
Solution 2
A man riding on a car has INERTIA of motion.

Question 3
What do you mean by inertia of rest?
Solution 3
When a body is at rest , it will continue to remain at rest unless some external force is applied to change its state of rest. This property of body is called inertia of rest.
Question 4
Name and state the action and reaction in the following cases:
(i) A book lying on a table,
(ii) A person walking on the ground,
(iii) Hammering a nail,
(iv) Firing a bullet from a gun,
(v) Pushing a wall.
Solution 4
(i) Weight of the book is action and normal force applied by table on book is reaction.
(ii) Force applied by man on ground is action and force of friction is the reaction.
(iii) Force applied by hammer on nail is action and normal force applied by nail on hammer is reaction to this force.
(iv) Firing of bullet is the action and recoiling of gun is the reaction.
(v) Force applied by us on wall is action and opposite force applied by wall on us or we can say that resistance of wall to our force is reaction.

Question 5
Give two examples of each:
(i) Inertia of rest, and
(ii) Inertia of motion
Solution 5
A book lying on a table will remain placed on  table unless it is displaced by some external force. This is an example of inertia of rest.
A ball rolling on the ground  will continue to roll unless the external force , the force of friction between the ball and the ground stops it.This is an example of inertia of motion.
Question 6
What causes motion in a body?
Solution 6
Unbalance external force causes motion in the body.

Question 7
What do you mean by linear momentum of a body?
Solution 7
Linear Momentum is defined as the amount of motion contained in a body. It is given by the product of the mass of the body and its velocity.
Question 8
Write the SI unit of momentum.
Solution 8
SI unit of momentum is kgms-1.

Question 9
Give qualitative definition of force on the basis of Newton's first law of motion.
Solution 9
According to Newton's first law force is that external agency which tends to change the state of rest or the state of motion of a body.
Question 10
State Newton's first law of motion.
Solution 10
According to Newton's first law, everybody continues in its state of rest or in uniform motion in a straight line unless compelled by some external force to act otherwise.

Question 11
Define one Newton.
Solution 11
1 Newton is the force which when applied to a body of unit mass produces a unit acceleration in it.
Question 12
What is the relation between Newton and dyne?
Solution 12
Newton is the SI unit of force whereas  dyne is the CGS unit of force.
1 N = 105 dyne.

Question 13
Is force a scalar quantity?
Solution 13
No, force is a vector quantity.
Question 14
A force can produce ------. In an object at rest. It can ------ an object and change its ------- of motion.
Solution 14
A force can produce MOTION in an objectat rest. It can ACCELERATE an object and can change its DIRECTION of motion.

Question 15
What does a force do in the following cases?
(a) You pull the skin of your arm.
(b) You twist a piece of rubber.
(c) You apply brakes to a running car.
(d) You catch a kicked ball.
Solution 15
(a) force changes  the shape of skin.
(b) force produces  stretching in the rubber.
(c) force provides retardation to the car and finally stops the car.
(d) force decreases  the momentum of ball and finally stops the ball.
Question 16
Can every force produced motion in every type of body?
Solution 16
No, every force does not produce motion in every type of body.

Question 17
The amount of inertia of a body depends on its ----------.
Solution 17
The amount of inertia of a body depends on its MASS.
Question 18
You can change the direction in which an object is moving by -----------.
Solution 18
You can change the direction in which an object is moving  by APPLYING FORCE ON IT.

## Chapter 3 - Laws of Motion Exercise 129

Question 1
Which of the following has the largest inertia?
(i) A car
(ii) A truck
(iii) A cricket ball
(iv) A ball pen
Solution 1
Out of all these, as mass of truck is greatest and mass is measure of inertia so a truck has maximum inertia.
Question 2
Why is it advantageous to turn before taking a long jump?
Solution 2
It is advantageous to run before taking a long jump because after running we get motion of inertia which helps in long jumping.

Question 3
Why does a ball moving on a table top eventually stops?
Solution 3
Ball moving on a table top stops eventually due to force of friction between the ball surface and table surface.
Question 4
Name the physical quantity which equals the rate of change of linear momentum.
Solution 4
Force is equal to the rate of change of linear momentum.

Question 5
State Newton's second law of motion. Is Newton's first law of motion contained in Newton's second law of motion?
Solution 5
According to newton second law of motion, when a force acts on a body, the rate of change in momentum of a body is equal to the product of mass of the body and acceleration produced in it.
Yes, Newton's first law is contained in the second law as if force is zero then acceleration would be zero which means body would remain in its state of rest or in state of constant motion.
Question 6
Define one newton.What is the ratio of SI to CGS units of force?
Solution 6
1 Newton is the force which when applied to a body of unit mass produces a unit acceleration in it.
1 newton / 1dyne = 105.

Question 7
Prove that 1 N = 105 dyne. Is 1 N same as 1 kgms-2?
Solution 7
1 newton = 1 kg X 1 ms-1 = 1000 g X 100 cms-1 = 105 cms-1.
1 dyne 1 g X 1 cms-1 = 1cms-1.
So 1 newton = 105 dyne.
Question 8
Two equal and opposite forces acting at the same point on a stationary body. Will the body move? Give reason to explain your answer.
Solution 8
No, the body will not move as the two forces are equal and opposite and they constitute balanced forces.

Question 9
Two equal and opposite forces act on a moving body. How is its motion affected?
Solution 9
As these forces are balanced so they will not affect the motion and motion of the body will remain unaffected.
Question 10
State Newton's third law of motion. Explain, the motion of a rocket with the help of Newton's third law of motion.
Solution 10
According to Newton's third law, for every action there is always an equal and opposite reaction. Rocket works on the same principle. The exhaust gases produced as the result of the combustion of the fuel are forced out at one end of the rocket. As a reaction , the main rocket moves in the opposite direction.

Question 11
A boy pushes a wall with a force of 30 N towards east. What force is exerted by the wall on the boy?
Solution 11
According to Newton's third law, every action has equal and opposite reaction so force exerted by the wall on the boy is 30 N.
Question 12
Name the scientist who first stated the law of inertia.
Solution 12
Newton stated the law of inertia.

Question 13
State the law of gravitation. Why is it called universal?
Solution 13
Every object in the universe attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of distance between them.
Law of gravitation is called universal because it applies to all bodies of universe.
Question 14
What is the difference between gravity and gravitation?
Solution 14
Gravity is the force of attraction betwen the object and the earth whereas gravitation refers to the force of attraction that exists between any two bodies that possess mass.

Question 15
Where will a person weigh more: at Simla or at Delhi?
Solution 15
Person will weigh more at Delhi as we know that gravity decreases with increase in height. Now as Shimla is at a height from Delhi so weight is less in Shimla and more in Delhi.
Question 16
Name the instrument used to measure the weight of a body.
Solution 16
Spring scale is used to measure the weight of a body.

Question 17
Gravity is another kind of --------- . It exerts all through the ------------. The Sun's gravity keeps the --------- in their orbits. Gravity can only be felt with very large----------.
Solution 17
Gravity is another kind of FORCE. It exerts all through the UNIVERSE. The sun's gravity keeps  the PLANETS in their orbits. Gravity can only be felt with very large MASS.
Question 18
Explain why:
(a) Objects fall to the earth.
(b) The atmosphere does not escape.
(c) A moon rocket needs to reach a certain velocity.
Solution 18
(i) Objects fall on the earth due to gravitational force between the earth and object.
(ii) Atmosphere doesnot escape because molecules of atmosphere are attracted by earth due to gravitational force of earth.
(iii) A moon rocket needs to reach a certain velocity because during its motion earth attracts the rocket towards it by its gravitational force.

Question 19
Explain the difference between g and G.
Solution 19
'g' is acceleration due to earth's gravity and 'G' is universal gravitational constant.
Question 20
What do you understand by the free fall?
Solution 20
Free fall means motion of a body under the gravity of earth only.

Question 21
Is there a gravitational attraction between you and the book? Explain.
Solution 21
Yes, we have a gravitational force of attraction between us and a book. But our mass is very small so the force between us and book is very small almost negligible.
Question 22
Does the force of the earth's gravitation affect the motion of the moon? Explain your answer with reasons.
Solution 22
Yes, the force of gravitation of earth affects the motion of moon, because moon is revolving around earth and centripetal force for this revolution is provided by earth's gravitation.

Question 23
Differentiate between gravitational mass and inertial mass.
Solution 23
Inertial mass is measure of inertia of the object. According to second law of motion F = m X a
m= F/a and this mass is called as inertial mass.
Newton law of gravitation gives another definition of mass.
F = (G m1m2)/R2
Thus m2 is the mass of the body by which another body of mass m1 attracts it towards it by law of gravitation. This mass is called gravitational mass.
Question 24
State Newton's law of gravitation. What is the difference between
(i) Gravity and gravitation
(ii) g and G?
Solution 24
Newton law of gravitation is that Every object in the universe attracts every other object with a force directly proportional to the product of their masses  and inversely proportional to the square of distance between them.
(i) Gravity is the force of attraction between the object and the earth whereas gravitation refers to the force of attraction that exists between any two bodies that possess mass.

(ii) 'g' is acceleration due to earth's gravity and 'G' is universal gravitational constant.

Question 25
An apple falls towards the earth due to its gravitational force. The apple also attracts the earth with the same force. Why do we not see the earth rising towards the apple? Explain.
Solution 25
Yes, it is true that apple attracts the earth towards it with same force but the mass of earth is so huge that acceleration produced in it due to this force is very much small and negligible to notice.
Question 26
In fig. 1, a block of weight 20 N is hanging from a rigid support by a string. Find:
(a) The force exerted by block on the string.
(b) The force exerted by string on the block.
Solution 26
(i) The force exerted by the block on is the weight of box and that is equal to 20N.
(ii) The force exerted by string on block is equal to the tension in the string and this is also equal to the 20N.

Question 27
A force of 4 N gives a mass m1 an acceleration of 8 ms-2 and a mass m2 an acceleration of 20 ms-2. What would be the acceleration if the same force acts on both the masses tied together?
Solution 27
we know F = m X a
m= F/a
so we can calculate mass of each body
Mass of body 1 m1 = 4/8 = 0.5 kg.
Mass of body 2  m2  = 4/20  = 0.2 kg.
Total mass when two masses are tied together  M = 0.5 + 0.2 = 0.7 kg.
Now as force is acting on total mass so acceleration produced is
a=  4/0.7 = 5.71 ms-2.

Solution 1
Solution 2
Solution 3

## Chapter 3 - Laws of Motion Exercise 130

Question 1
Solution 1
Question 2
A force of 0.9 N acting on a body increases its velocity from 5 ms-1 to 8 ms-1 in 2 s. Calculate the mass of the body.
Solution 2
Initial speed of body = 5 ms-1
Final speed of body = 8 ms-1
Time taken to acquire this speed = 2 s.
Acceleration of body = ( v- u)/t
a= (8- 5)/2 = 1.5 ms-2.
Force applied on body = 0.9 N.
we know F = m X a.
m = f/a = 0.9/1.5 = 0.6 kg
mass of the body is 600 gm.

Question 3
Solution 3
Question 4
What do you mean by an impulsive force?
Solution 4
The force that acts on a body for a very short time but produces a large change in its momentum, is known as impulsive force.

Question 5
For how long should a force of 100 N act on a body of mass 20 kg so that it acquires a velocity of 100 ms-1?
Solution 5
initial velocity of body = 0 ms-1.
Final velocity of body = 100 ms-1.
Mass of body = 20 kg.
Force applied = 100N.
We know that
F X t = m (v - u)
100 t = 20 (100 -0)
T = 2000/100 = 20 s.
Question 6
Write the SI unit of retardation.
Solution 6
SI unit of retardation is ms-2.

Question 7
What is the relationship between force and acceleration?
Solution 7
Force applied is equal to the product of mass and acceleration produced in the body.
F = mass X acceleration.
Question 8
State Newton's second law of motion.
A body of mass 400 g is resting on a frictionless table. Find the acceleration of the body when acted upon by a force of 0.02 N.
Solution 8
According to Newton's second law of motion, when a force acts on a body, the rate of change in momentum  of a body equals the product of mass of the body and acceleration produced in it due to that force, provided the mass remains constant.
Mass of  body = 400 g = 0.4kg
Force applied on body = 0.02 N
Acceleration = force/mass = 0.02/0.4 = 0.05 ms-2.

Question 9
What do you mean by linear momentum of a body? A force causes an acceleration of 10 ms-2 in a body of mass 1 kg. What acceleration will be caused by the same force in a body of mass 4 kg?
Solution 9
Linear Momentum is defined as the physical quantity which is associated with bodies in linear motion. It is given by the product of the mass of the body and its velocity.
Mass of body = 1 kg
Acceleration produced = 10 ms-2.
Force applied would be = 1 X 10 N = 10 N.
Mass of second body = 4 kg.
As same force has to be applied on second body so force = 10N.
Acceleration produced is = F/M =10/4 = 2.5 ms-2.
Question 10
Two bodies P and Q, of same masses m and 2m are moving with velocities 2 v and v respectively. Compare their (i) Inertia, (ii) Momentum, and (iii) The force required to stop them in the same time.
Solution 10
Mass of P is m1= m.
Velocity of P is v1 =2 v
Mass of Q is m2 = 2m
Velocity of Q is v2 = v.
(i) inertia of P/inertia of Q = m1/m2 = 1/2.
So ratio of inertia of two bodies is 1:2.
(ii) Momentum of P/momentum of Q = m1v1/m2v2 =  1
So ratio of momentum of two bodies is 1:1.
(iii) As force required to stop them is equal to change in their momentum from moving to rest.
So ratio would be same as the ratio of their momentum i.e 1: 1.

Question 11
Show that the rate of change of momentum = mass X acceleration. Under what condition does this relation hold?
Solution 11
According to newton second law
F = m X a
a= (v - u)/t.
F = m(v -u)/t
F = (mv - mu)/t
As F= m X a
ma = (mv - mu)/t
so rate of change of momentum = mass X acceleration.
This relation holds good when mass remains constant during motion.
Question 12
What do you mean by the conservation of momentum? Briefly, explain the collision between two bodies and the conservation of momentum.
Solution 12

Question 13
State Newton's third law of motion. Give an experimental demonstration of Newton's third law.
Solution 13
According to newton third law, for every action there is always an equal and opposite reaction.
To demonstrate newton third law blow a balloon and hold its neck tightly facing downwards. When we release the balloon, the balloon will moves up instead of falling  to the ground. As air is releasing from bottom of balloon and this air apply equal and opposite force to the balloon and this force helps balloon to move upwards.
Question 14
A force acts for 0.1 s on a body of mass 2.0 kg initially at rest. The force is then withdrawn and the body moves with a velocity of 2 ms-1. Find the average force applied by the player.
Solution 14
time for which force is applied = 0.1 s.
Mass of body = 2 kg
Initial velocity of body = 0 ms-1
Final velocity of body = 2 ms-1.
We know FX t = m (v - u)
F X 0.1 = 2 (2 - 0)
F = 4 /0.1 = 40 N.

Question 15
A cricket ball of mass 500 g moving at a speed of 30 ms 1 is brought to rest by a player in 0.03 s. Find the average force applied by the player.
Solution 15
mass of ball = 500g = 0.5 kg.
Initial speed of the ball = 30 ms-1
Final speed of ball = 0 ms-1
Time taken by player to stop the ball = 0.03 s.
We know FX t = m (v - u)
F X 0.03 = 0.5 (0 - 30)
F = - 1.5 / 0.03 = - 500 N
(- ) sign shows that player has to apply force in opposite direction of the motion of the ball.
Question 16
A force acts for 0.1 s on a body of mass 3.2 kg initially at rest. The force then ceases to act and the body moves through 3 m in the next one second. Calculate the magnitude of force.
Solution 16
Time for which force is applied =0.1 s.
Mass of the body = 3.2 kg.
Initial speed of body = 0 ms-1After removal of forces body covers a distance of 3m in 1 second so final speed of body = 3/1 = 3ms-1.
We know FX t = m (v - u)
F X 0.1 = 3.2 (3 -0)
F = 9.6/0.1 = 96 N.
So applied force is 96 N.

Question 17
Solution 17

## Chapter 3 - Laws of Motion Exercise 131

Question 1
A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate:
(i) The velocity acquired by the body, and
(ii) Change in momentum of the body.
Solution 1
Time for which force is applied =3 s.
Mass of the body = 2 kg.
Initial speed of body = 0 ms-1
Force applied = 10 N.
(i) We know F X t = m (v - u)
10 X3 = 2 (v- 0)
v = 15 ms-1.
Final velocity is 15 ms-1.
(ii) As m(v - u) is change in momentum and this is equal to the F X t so change in momentum is equal to the 30 kgms-1.
Question 2
Use Newton's second law to explain the following:
(i) We always prefer to land on sand instead of hard floor while taking a high jump.
(ii) While catching a fast moving ball, we always pull our hands backwards.
Solution 2
(i) We always prefer to land on sand instead of hard floor while taking a high jump because sand increases the time of contact.As FX t = m ( v - u ) and our change in momentum is constant so if time increases then force experienced would decrease.
(ii) Again while catching a fast moving ball, we always pull our hands backwards to increase reaction time so force experienced would decrease.

Question 3
A stone is dropped from a cliff 98 m high.
(a) How long will it take to fall to the foot of the cliff?
(b) What will be its speed when it strikes the ground?
Solution 3
Height of cliff = 98 m.
Initial velocity of stone = 0 ms-1.
Acceleration due to gravity = 9.8 ms-2.

(i) We know H = ut + 1/2 gt2.
98 = 1/2 X 9.8X t2.
t2 = 98X2/9.8 = 20
t= 4.47 sec.
(ii) Final velocity when it strikes the ground
V2 - u2 = 2 g H
V2 = 2X9.8X98
V2= 1920
V= 44.6 ms-1.
Question 4
A stone is thrown vertically upward with a velocity of 9.8 m/s. When will it reach the ground?
Solution 4
Initial speed of ball is = 9.8 ms-1.
Acceleration due to gravity = -9.8 ms-2.
Final speed at maximum height = 0 ms-1.
We know v = u + at
0 = 9.8 - 9.8 t
T = 1 sec.
We know v2 - u2 =2as
At highest point final velocity is zero so
0 - 9.8 X 9.8 = 2 X (-9.8) S
S = 4.9 m.
for highest point initial velocity is zero
Acceleration due to gravity is = 9.8 ms-2.
Final velocity at ground is v
V2 - 0 = 2 X9.8 X 4.9
V = 9.8 ms-1.
Time taken to reach ground from highest point
V = u + at
9.8 = 0 + 9.8 t
T = 9.8/9.8 = 1 sec.
Total time = time of ascent + time of descent.
Total of flight = 1+ 1 = 2 seconds.

Question 5
A ball is thrown vertically downward with an initial velocity of 10 m/s. What is its speed 1 s later and 2 s later?
Solution 5
Initial speed of ball = 10 ms-1.
Acceleration due to gravity on ball = - 9.8 ms-2
We know that from first equation of motion
v= u + gt.
After 1 sec
v= 10 - 9.8 X1
v= 0.2 ms-1
so velocity after 1 sec would be 0.2 ms-1.

Velocity after 2 seconds
v= 10 - 9.8X2 = 10 - 19.6 = -9.6 ms-1.
Here negative sign shows that velocity is in downward direction and magnitude is 9.6 ms-1.
Question 6
A ball is thrown upward and reaches a maximum height of 19.6 m. Find its initial speed?
Solution 6
Maximum Height attained by ball = 19.6 m
Let initial speed of ball = u ms-1.
Acceleration applied on ball due to gravity = -9.8 ms-2.
Final speed of ball at maximum height = 0 ms-1.
We know that from second equation of motion
V2 - u2 = 2as
0 -u2 = 2 X(-9.8)X19.6
u2 = 19.6 X 19.6
u= 19.6 ms-1
so initial speed of ball to attain maximum height of 19.6 m should be 19.6ms-1.

Question 7
A stone is dropped from a tower 98 m high. With what speed should a second stone be thrown 1 s later so that both hit the ground at the same time?
Solution 7
Height of tower = 98 m
Acceleration due to gravity on stone = 9.8 ms-2.
Initial speed of ball= 0 ms-1.
Let initial speed of second stone is v ms-1.
We know from second equation of motion
S = ut + 1/2 a Xt2.
98 = 0 + 1/2 X9.8Xt2.
t2 = 20
t= 4.47 sec.
As second stone is thrown 1 sec later so time taken by second body to cover distance of 98 m is = 4.47 - 1 = 3.47sec.
So again put t= 3.47 sec and S = 98 m in second equation of motion we get
98 = vX3.47 + 1/2 X9.8X3.47X3.47.
98 = 3.47Xv + 59
3.47X v = 98 - 59
v= 39/3.47 = 11.23 ms-1.
Initial speed of second stone should be 11.23 ms-1.