# NCERT Solutions for Class 9 Science Chapter 9 Force and Laws of Motion

NCERT solutions for class 9 science chapter 9 Force and Laws of Motion:  This chapter will help you to understand the concepts of force and laws of motion. Have you ever thought about what causes a body to move? How can we stop a moving body? How can we change the direction of a body? The answer to all the three questions is by applying a force. With the help of solutions for NCERT class 9 science chapter 9 Force and Laws of Motion, you will be able to understand the concepts of the chapter. Along with this chapter's solutions, you can also check NCERT solutions for other chapters and subjects. CBSE NCERT solutions for class 9 science chapter 9 Force and Laws of Motion, will help you to understand Newton's 3 laws of motion and another main topic inertia. For a better understanding of these concepts, you can read daily life examples related to Newton's law and inertia are created by our experts.

i) Newton's first law of motion:

Everybody continues its state of uniform motion along a straight line or state of rest unless acted by an external force. For example, if we hit a resting ball it will move and will not stop unless there is an external force. The external force acting here is friction which opposes the motion of the ball.

ii) Momentum

The momentum of a body is the product of its mass and velocity.

Newton's second law of motion: The rate of change of momentum of a body is directly proportional to the unbalanced force applied in the direction of the force.

If a body of mass m is moving with initial velocity u along a straight line. It is uniformly accelerated to a velocity v by applying a force for time t then, the rate of change of momentum = force applied. That is force applied

$F=\frac{m(v-u)}{t}$

iii) Newton's third law of motion

Newton's third law of motion states that every force has equal and opposite reactions. For example, when a bullet is fired from a gun, the gun exerts a forward force on the bullet and the bullet exerts a backward force on the gun. That is why the gun moves back (recoil of the gun) when fired.

iv) Interia: The inertial of an object is its natural tendency to continue its state of rest or motion. Mass is the measure of the inertia of an object. For example, when a moving bus applies brake  people in the bus moves forward, this is due to the inertia of motion

The main topics of NCERT Solutions for Class 9 Science Chapter 9 Force and Laws of Motion are:

9.1 Balanced and Unbalanced Forces

9.2 First Law of Motion

9.3 Inertia and Mass

9.4 Second Law of Motion

9.5 Third Law of Motion

9.6 Conservation of Momentum

The answer given herein for the questions mentioned at the end of the chapter will help you to revise the chapter. As per the CBSE syllabus & exam pattern, the chapter 9 Force and Laws of Motion is a part of 3rd unit, Motion, Force and work carry weightage of 27 marks in the final exam of class 9.

## NCERT solutions for class 9 science chapter 9 Force and Laws of Motion

### Topic 9.3 Inertia and Mass

(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-rupee coin?

We know that inertia is defined by the mass of the body. So the body has more mass/weigth will have more inertia.

(a) In the case of rubber ball and stone of the same size, the stone will have greater mass so its inertia will be more as compared to a rubber ball.

(b) The train has much more mass as compared to the bicycle so the inertia of the train is larger.

(c) A five rupees coin has more weight than one rupee coin so the inertia of five rupees coin is more.

“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.

Velocity has both magnitude and direction. Thus change in any of magnitude or direction results in a change in velocity.

In the given case, when the player kicks the ball to another player the direction of the ball is changed thus velocity is changed.

The second player then pushes the ball in a forward direction, so velocity changes. Then the goalkeeper brings ball at rest hence velocity changes (magnitude is changed). After that he kicks the ball thus increase the speed and direction is opposite, hence velocity changes again.

The agent of supplying force is 1st player, 2nd player, goalkeeper, and goalkeeper respectively.

This can be explained with the help of the concept of inertia. When the tree is at rest, its leaves are also at rest. But when we bring the tree in motion by means of shaking it, due to the inertia of leaves they still tend to be in rest. Thus force is acting on leaves vigorously with changing direction rapidly. This results in detaching of leaves from the tree.

In the situation of a moving bus, the passengers are also in motion along with the bus. Now when brakes are applied the bus comes to rest but due to the inertia of passengers they still tend to move in the forward direction, Thus they move in the forward direction after applying brakes.

Now when the bus is rest, the passengers are also at rest. The inertia tend them to be at rest. That's why when bus accelerates they move in a backward direction.

## NCERT textbook solutions for class 9 science chapter 9 Force and Laws of Motion

Topic law of Motion

For motion, horse applies force on the ground and thus the frictional force of the ground pushes the horse forward (action-reaction pair). Thus horse applies force on the cart and cart applies backward force on the horse but due to unbalanced force, the horse moves in the forward direction.

This can be explained with the help of Newton's third law of motion (action-reaction pair). When the velocity of water is more i.e., water is coming out with higher force thus the reaction force on the hose is also large. This makes it difficult for a fireman to hold the hose.

Here we will use conservation of momentum :

Initial momentum of system ( rifle + bullet )    =   Final momentum of system

$m_1u_1\ +\ m_2u_2\ =\ m_1v_1\ +\ m_2v_2$

or $4\times 0\ +\ 0.05\times 0\ =\ 4\times v_1\ +\ 0.05\times 35$

or  $-4 \times v_1\ =\ 1.75$

or  $v_1 \ =\ -\ 0.4375\ m/s$

The negative sign shows that velocity is opposite to that of the bullet. This is because the force on the rifle will be opposite by bullet (action-reaction pair).

In this question we will use conservation of momentum :

Initial momentum   =  Final momentum

$m_1u_1\ +\ m_2u_2\ =\ m_1v_1\ +\ m_2v_2$

or  $0.1\times 2\ +\ 0.2\times 1\ =\ 0.1\times 1.67\ +\ 0.2\times v_2$

or       $v_2\ =\ \frac{0.233}{0.2}$

or       $v_2\ =\ 1.165\ m/s$

Hence required velocity is 1.165 m/s.

## Free NCERT solutions for class 9 science chapter 9 Force and Laws of Motion- Excercise solution

When a net zero external unbalanced force is applied and the object is in motion then there will be a condition in which its motion is unopposed by any external force. Then as a result object will continue to remain in motion. The velocity, in this case, will be constant and in a particular direction.

During beating the carpet we bring it in the motion. But the dust particles have a tendency to be at rest so they resist the motion. This is why they come out of the carpet. The factor responsible for this is inertia.

This is because the luggage has some mass so the inertia. When the bus is in motion, the luggage is also in motion. But when the bus stops suddenly, the luggage still tends to move with the same velocity due to inertia. Thus it may fell down. Similarly, when the bus starts from the rest, the luggage tends to be in rest thus it is pushed in a backward direction.

(a) the batsman did not hit the ball hard enough.

(b) velocity is proportional to the force exerted on the ball.

(c) there is a force on the ball opposing the motion.

(d) there is no unbalanced force on the ball, so the ball would want to come to rest

The frictional force present between the ground and the ball acts in the opposite direction of the motion of the ball. Thus balls stop after traveling a few distances.

Hence option (c) is correct.

From the equations of motion we can write :

$s\ =\ ut\ +\ \frac{1}{2}at^2$

or    $400\ =\ 0\times 20\ +\ \frac{1}{2}\times a\times 20^2$

or     $a\ =\ \frac{400}{200}\ =\ 2\ m/s^2$

And the force acting on the truck is given by :

$F\ =\ ma$

$=\ 7000\times 2$

$F\ =\ 14000\ N$

By the equation of motion, we know that,

$v^2\ =\ u^2\ +\ 2as$

or  $0^2\ =\ 20^2\ +\ 2a\times 50$      (Since ball comes to rest thus final velocity is zero.)

or$a\ =\ \frac{-400}{100}\ =\ -4\ m/s^2$

The acceleration is negative. This implies that the force is opposing the motion.

The force is given by :

$F\ =\ ma$

or    $F\ =\ 1\times \ (-4)\ =\ -4\ N$

Hence the frictional force between stone and ice is 4 N.

The net accelerating force is given by :

Net accelerating force    =    Force by engine    -    Frictional force

$=\ 40000\ -\ 5000\ =\ 35000\ N$

We know that the force is given by :

$F\ =\ ma$

or                                 $35000\ =\ (8000\ +\ 10000)a$

or                                         $a\ =\ \frac{35000}{18000}\ =\ 1.944\ m/s^2$

Thus acceleration of the train is   $1.944\ m/s^2$.

By Newton's law of motion, we have :

$F\ =\ ma$

and    $=\ 1500\times 1.7$

or  $F\ =\ -2550\ N$

Thus the retarding force required is 2550 N in the direction opposite to the motion of the vehicle

(a) $(mv)^{2}$  (b) $mv^{2}$     (c) $\frac{1}{2}mv^{2}$  (d) $mv$

We know that the momentum of a body is given by:-

Momentum    =    Mass $\times$  Velocity

Thus we have : $p\ =\ mv$

Hence option (D) is correct.

By Newton's third law it is clear that the frictional force acting on the cabinet will be 200 N. (Note that the limit of frictional force depends upon mass of body and the coefficient of friction between the bodies. So it might be possible that if frictional force acting is less than 200 N).

The velocity of the combined mass after the collision will be zero.

This can be found using the law of conservation of the momentum :

$m_1u_1\ +\ m_2u_2\ =\ (m_1\ +\ m_2)v$

or  $mu\ +\ m(-u)\ =\ (2 m)v$

or    $2mv\ =\ 0$

Thus $v\ =\ 0$

The student is correct. The force applied by him is less than the static friction present between tyres of the truck and the road (as the mass of truck is large thus the frictional force is also high). Thus the force applied by the student is balanced by the static frictional force which is the action-reaction pair.

The change in the momentum is given by :

$\Delta p\ =\ m\Delta v$

or   $=\ 0.2\times (-5\ -\ 10)$

or   $=\ -3\ Kg\ m/s$

In the above equation, we have taken   $v\ =\ -5\ m/s$    as its direction is opposite.

By the equation of motion we know that:-

$v\ =\ u\ +\ at$

Putting values of v, u and t in the equation :

$0\ =\ 150\ +\ a\times 0.03$

or        $a\ =\ \frac{-150}{0.03}$

or      $a\ =\ -5000\ m/s^2$

Now we have :

$s\ =\ ut\ +\ \frac{1}{2}at^2$

or         $=\ 150\times 0.03\ +\ \frac{1}{2}\times (-5000)\times 0.03^2$

or   $=\ 2.25\ m$

Hence the distance of penetration of the bullet in the block is 2.25 m.

Now for the force we have :

$F\ =\ ma$

or   $=\ 0.01\times (-5000)\ =\ -50\ N$

Thus the retarding force acting on the bullet is 50 N.

For calculating the velocity of the combined mass we need to use the law of conservation of momentum.

$m_1u_1\ +\ m_2u_2\ =\ (m_1\ +\ m_2)v$

or     $1\times 10\ +\ 5\times 0\ =\ (1\ +\ 5)v$

or  $v\ =\ \frac{10}{6}$

or      $v\ =\ 1.66\ m/s$

Now, the momentum before the collision is :

$p_i\ =\ m_1u_1\ +\ m_2u_2$

or   $=\ 1\times 10\ +\ 5\times 0\ =\ 10\ Kg\ m/s$

By momentum conservation, final momentum is also    $10\ Kg\ m/s$

The momentum is given by :

$p\ =\ mv$

Initial momentum is : $p_i\ =\ mu\ =\ 100\times 5\ =\ 500\ Kg\ m/s$

And the final momentum is :

$p_f\ =\ mv\ =\ 100\times 8 \ =\ 800\ Kg\ m/s$

Also, the force is defined as rate of change of momentum.

Thus  $F\ =\ \frac{p_f\ -\ p_i}{t}$

or   $=\ \frac{800\ -\ 500}{6}\ =\ 50\ N$

Hence the force exerted on the body is 50 N.

Kiran’s observation:-   The insect experiences a greater change in its velocity as the mass of insects is much less as compared to the motorcar so it experiences a greater change in its momentum. Thus Kiran's observation is correct.

Akhtar’s observation:-   We know that motorcar has a larger velocity and has a bigger mass as compared to the insect. Also, the motorcar continues to move in the same direction even after the collision. This suggests that the change in momentum of a motorcar is very less, whereas the insect experiences a great change in its momentum.

Rahul’s observation:-   The momentum gained by the insect is equal to the momentum lost by the motorcar (law of conservation of momentum). Thus his observation is also correct.

For calculating momentum, we need the final velocity of the bell.

By equation of motion we can write :

$v^2\ =\ u^2\ +\ 2as$

or   $v^2\ =\ 0^2\ +\ 2\times 10\times 0.8$

or   $v\ =\ 4\ m/s$

Thus the momentum is :   $p\ =\ mv$

or  $=\ 10\times 4\ =\ 40\ Kg\ m/s$

## CBSE NCERT solutions for class 9 science chapter 9 Force and Laws of Motion - Additional Exercises

•  What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero?
 Time in seconds Distance in metre 0 0 1 1 2 8 3 27 4 64 5 125 6 216 7 343

From the table, the relation between time and distance can be seen.

$s\ =\ t^3$

Thus the velocity of the particle is increasing with time.

$v\ =\ \frac{ds}{dt}\ =\ 3t^2$

and                                                               $a\ =\ \frac{dv}{dt}\ =\ 6t$

Hence acceleration increases linearly with time.

## Q A1.(b)    The following is the distance-time table of an object in motion:

 Time in seconds Distance in metre 0 0 1 1 2 8 3 27 4 64 5 125 6 216 7 343

i)Velocity is the change in distance with time. So the velocity is increasing non uniformly, so the acceleration increases with the time.

$F\ =\ ma$

ii) Thus the net force acting on the body is also increasing.

From the question, it is clear that two-person pushes the car with constant velocity. But when the third person pushes it has some acceleration. Thus the third person is responsible for the acceleration generated.

Force by the third person is given by :

$F\ =\ ma$

$=\ 1200\times 0.2\ =\ 240\ N$

Hence the force from each man is 240 N.

Thus the force is given by :

$\\F = m\frac{v-u}{t}\\=500\times10^{-3}(\frac{0-50}{0.01})=-2500N$

or      $=\ 0.5\times (-5000)\ =\ -2500\ N$

The negative sign implies that the force by the nail on the hammer is in the opposite direction.

The initial and final velocities are :

$u\ =\ 90\times \frac{5}{18}\ =\ 25\ m/s$

and                                                    $v\ =\ 18\times \frac{5}{18}\ =\ 5\ m/s$

Using the equation of motion we can write :

$v\ =\ u\ +\ at$

or                                                $5\ =\ 25\ +\ a\times 4$

or                                                $a\ =\ -5\ m/s^2$

Now the force is given by :

$F\ =\ ma$

or                                                    $=\ 1200\times (-5)\ =\ -\ 6000\ N$

And the change in momentum is :           $\Delta p\ =\ m\Delta v$

or                                                                       $=\ 1200(-20)\ =\ - 24000\ Kg\ m/s$

## NCERT Solutions for Class 9 Science- Chapter Wise

 Chapter No. Chapter Name Chapter 1 Solutions for NCERT class 9 science chapter 1 Matter in Our Surroundings Chapter 2 NCERT solutions for class 9 science chapter 2 Is Matter Around Us Pure Chapter 3 CBSE NCERT solutions for class 9 science chapter 3 Atoms and Molecules Chapter 4 NCERT textbook solutions for class 9 science chapter 4 Structure of The Atom Chapter 5 Free NCERT solutions for class 9 science chapter 5 The Fundamental Unit of Life Chapter 6 Solutions for NCERT class 9 science chapter 6 Tissues Chapter 7 NCERT solutions for class 9 science chapter 7 Diversity in Living Organisms Chapter 8 CBSE NCERT solutions for class 9 science chapter 8 Motion Chapter 9 NCERT solutions for class 9 science chapter 9 Force and Laws of Motion Chapter 10 NCERT textbook solutions for class 9 science chapter 10 Gravitation Chapter 11 Free NCERT solutions for class 9 science chapter 11 Work and Energy Chapter 12 CBSE NCERT solutions for class 9 science chapter 12 Sound Chapter 13 Solutions for NCERT class 9 science chapter 13 Why Do We Fall ill? Chapter 14 Free NCERT solutions for class 9 science chapter 14 Natural Resources Chapter 15 NCERT textbook solutions for class 9 science chapter 15 Improvement in Food Resources

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