RBSE Class 9 Science Important Questions Chapter 9 Force and Laws of Motion

Question 5.
A passenger in a moving train tosses a coin which falls behind him. It means that motion of the train is :
(a) accelerated
(b) uniform
(c) retarded
(d) along circular tracks
Answer:
(a) accelerated

Question 6.
An object of mass 2 kg is sliding with a constant velocity of 4 ms^-1 on a frictionless horizontal table. The force required to keep the object moving with the same velocity is :
(a) 32 N
(b) 0 N
(c) 2 N
(d) 8 N
Answer:
(b) 0 N

Question 7.
Rocket works on the principle of conservation of :
(a) mass
(b) energy
(c) momentum
(d) velocity
Answer:
(c) momentum

Question 8.
A water tanker filled up to 2/3 of its height is moving with a uniform speed. On sudden application of the brake, the water in the tank would:
(a) move backward
(b) move forward
(c) be unaffected
(d) rise upwards
Answer:
(b) move forward

Question 9.
What is the S.I. unit of momentum?
(a) Nm
(b) \(\frac{N k g}{m}\)
(c) \(\frac{N m}{s}\)
(d) \(\frac{k g m}{s}\)
Answer:
(d) \(\frac{k g m}{s}\)

Question 10.
Momentum of an object depends on :
(a) mass of the object
(b) displacement of the object
(c) time taken for displacement
(d) All of these
Answer:
(a) mass of the object

Question 11.
Which of the following is not a unit of force?
(a) Pound
(b) Dyne
(c) Joule
(d) Newton
Answer:
(c) Joule

Question 12.
Rate of change of momentum is equal to which of the following?
(a) Velocity
(b) Work
(c) Force
(d) Acceleration
Answer:
(c) Force

Question 13.
Two forces, F₁ = 4N and F₂ = 3N are acting perpendicular on an object of 5 Kg simultaneously. What will be the acceleration of the object?
(a) 2 ms^-2
(b) 3 ms^-2
(c) 1 ms^-2
(d) 1.4 ms^-2
Answer:
(c) 1 ms^-2

Question 14.
Two forces of 4N and 3N are acting on an object in opposite directions. What will be the magnitude of resultant force on the object?
(a) 5N
(b) 7N
(c) 1N
(d) between 1N and 7N
Answer:
(c) 1N

Question 15.
Fill in the blanks :
(a) Applying force makes the spring ...............
(b) Momentum of an object is the product of its ...............
(c) Total momentum of two objects in the process of collision remains ...............
(d) If the resultant of different forces acting on an object is equal to zero, then it is called ............... force.
Answer:
(a) expand
(b) mass and velocity
(c) conserved
(d) balanced

Question 16.
Match the column (A) with the column (B).

Column (A)	Column (B)
(i) Velocity	(a) Kg m-3
(ii) Density	(b) Kg m/s2
(iii) Force	(c) m/s
(iv) Momentum	(d) N/m2
(v) Pressure	(e) Kg m/s

Answer:

Column (A)	Column (B)
(i) Velocity	(c) m/s
(ii) Density	(a) Kg m-3
(iii) Force	(b) Kg m/s2
(iv) Momentum	(e) Kg m/s
(v) Pressure	(d) N/m2

Question 17.
Read the statements carefully and identify whether they are True or False-
1. We obtain a definition of force from third law of motion.
2. SI unit of momentum is Kg m/s.
3. Friction force always opposes the motion of an object.
4. Momentum of an isolated system changes with respect to time.
5. A ball rebounds after striking a hard floor due to Newton’s third law of motion.
Answer:
1. False
2. True
3. False
4. False
5. True

Very Short Answer Type Questions

Question 1.
Define force.
Answer:
It is a push or pull on an object that produces acceleration in the body on which it acts.

Question 2.
What is balanced force?
Answer:
When forces acting on a body from the opposite direction do not change the state of rest or of motion of an object, such forces are called balanced forces.

Question 3.
What is frictional force?
Answer:
The force that always opposes the motion of object is called force of friction.

Question 4.
What is inertia?
Answer:
The natural tendency of an object to resist a change in its state of rest or of uniform motion is called inertia.

Question 5.
State Newton’s first law of motion.
Answer:
An object remains in a state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force.

Question 6.
State Newton’s second law of motion.
Answer:
The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.

Question 7.
What is momentum?
Answer:
The momentum of an object is the product of its mass and velocity and has the same direction as that of the velocity. The SI unit is kg m/s. (p = mv)

Question 8.
State Newton’s third law of motion.
Answer:
To every action, there is an equal and opposite reaction and they act on two different bodies.

Question 9.
Which will have more inertia: a body of mass 10 kg or a body of mass 20 kg?
Answer:
A body of mass 20 kg will have more inertia, as mass is measure of inertia.

Question 10.
Name the factor on which the inertia of the body depends.
Answer:
Inertia of a body depends upon the mass of the body.

Question 11.
Name two factors which determine the momentum of a body.
Answer:
Two factors on which momentum of a body depend is mass and velocity. Momentum is directly proportional to the mass and velocity of the body.

Question 12.
What decides the rate of change of momentum of an object?
Answer:
The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.

Question 13.
Why do athletes run some distance before jumping?
Answer:
Athlete has the inertia of motion and thus continues to move past the line.

Question 14.
How is inertia measured quantitatively?
Answer:
Quantitatively the inertia of an object is measured by its mass.

Question 15.
The fruits fall off the branches when a strong wind blows. Give reason.
Answer:
Fruits tend to continue in the state of rest on account of inertia while branches suddenly come into motion.

Question 16.
Name the physical quantity which is determined by the rate of change of linear momentum.
Answer:
Force.

Question 17.
Why action and reaction do not cancel each other?
Answer:
Action and reaction act simultaneous but on different objects. Hence, they do not cancel each other.

Question 18.
If a man jumps out from a boat, the boat moves backwards. Why?
Answer:
When a man jumps out of a boat to the bank of the river, he supplies a force in the forward direction. Due to the reaction of this, the boat moves backwards.

Question 19.
Explain our walking in terms of Newton’s third law of motion.
Answer:
When we walk on ground, our foot pushes the ground backward and in return the ground pushes our foot forward. The forward reaction exerted by the ground on our foot makes us walk forward.

Question 20.
There are three solid balls, made up of aluminium, steel and wood of the same shape and volume. Which of them would have highest inertia? Why?
Answer:
Steel ball because the density of steel is maximum. For the same shape and volume, steel ball will have maximum mass.

Question 21.
It is easier to push an empty box than to push the box full of hooks. Give reason.
Answer:
This is because the empty box has less inertia of rest than the box full of books.

Question 22.
Why all cars are provided with seat belts?
Answer:
Sudden movement of the vehicle results in the sudden change in the state of motion of the vehicle when our feet are in contact with it. But the rest of our body opposes this change due to its inertia and tends to remain where it was. Seat belts are provided to protect the passengers from falling backward or forward during such situation.

Question 23.
No force is required to move an object with a constant velocity. Why?
Answer:
For an object moving with a constant velocity, a = 0, so F = ma = 0

Question 24.
Why are road accidents at high speeds very much worse than accidents at low speeds?
Answer:
The time of impact of vehicles is very small at high speed. So, they exert very large forces on each other. Hence, road accidents at high speeds are very much worse.

Question 25.
Is force a scalar quantity or a vector quantity?
Answer:
Force is a vector quantity. It has both magnitude and direction.

Question 26.
Define SI unit of force.
Or
What is one Newton force?
Answer:
A Newton force is that force which act on a body of mass of 1 kg to produce an acceleration of 1 ms^-2 in it.

Question 27.
Two similar trucks are moving with the same velocity on a road. One of them is loaded while the other one is empty. Which of the two will require a larger force to stop it?
Answer:
The loaded truck will require a larger force to stop because it has greater momentum.

Question 28.
Name the scientist who introduced the property of momentum.
Answer:
Newton.

Question 29.
What is the direction of momentum?
Answer:
The direction of momentum is the same as that of velocity.

Question 30.
Which type of force does not change the state of rest or of motion of an object?
Answer:
Balanced force.

Question 31.
Which type of force brings an object in motion?
Answer:
Unbalanced force.

Short Answer Type Questions

Question 1.
Why we tend to get thrown to one side when a motorcar makes a sharp turn at a high speed?
Answer:
We tend to get thrown to one side when a motorcar makes a sharp turn at a high speed due to law of inertia. When we are sitting in moving car on a straight road, we tend to continue in our straight line motion. But when an unbalanced force is applied on car to change the direction of motion, we slip to one side of the seat due to the inertia of our body.

Question 2.
Why do fielders pull their hand gradually with the moving ball while - holding a catch?
Answer:
While catching a fast moving cricket ball, a fielder on the ground pulls his hands backwards with the moving ball. This is done so that the fielder increases the time during which the high velocity of the moving ball decreases to zero. Thus, the acceleration of the ball is decreased and therefore, the impact of catching the fast moving ball is reduced.

Question 3.
Why are athletes made to fall either on a cushioned bed or on a sand bed in a high jump athletic event?
Answer:
In a high jump athletic event, athletes are made to fall either on a cushioned bed or on a sand bed so as to increase the time of the athlete’s fall to stop after making the jump. This decreases the rate of change of momentum and hence the force.

Question 4.
Why are roads on mountains inclined inwards at turns?
Answer:
A vehicle moving on mountains is in the inertia of motion. At a sudden turn there is a tendency of vehicle to fall off the road due to sudden change in the line of motion hence the roads are inclined inwards so that the vehicle does not fall down the mountain.

Question 5.
Why you get hurt by hitting a stone while when you kick a football it flies away?
Answer:
This is because stone is heavier than football and heavier objects offer larger inertia. When we kick a football its mass is less and inertia is also less so force applied by our kick acts on it and hence it shows larger displacement but in case of stone, it has more mass and offers larger inertia. When we kick (action) the stone it exerts an equal and opposite force (reaction) and hence it hurts the foot.

Question 6.
What is the relation between Newton’s three laws of motion?
Answer:

• Newton’s first law explains about the imbalanced force required to bring change in the position of the body.
• Second law explains about the amount of force required to produce a given acceleration.
• While, Newton’s third law explains how these forces acting on a body are interrelated.

Question 7.
Give any three examples in daily life which are based on Newton’s third law of motion.
Answer:
Three examples based on Newton’s third law are :
Swimming: We push the water backward to move forward.

• Action - Water is pushed behind.
• Reaction - Water pushes the swimmer ahead.

Firing gun: A bullet fired from a gun and the gun recoils.

• Action - Gun exerts force on the bullet.
• Reaction - Bullet exerts an equal and opposite force on the gun.

Launching of rocket:

• Action - Hot gases from the rocket are released.
• Reaction - The gases exert upward push to the rocket.

Question 8.
Why does a fireman struggle to hold a hose-pipe?
Answer:
A fireman has to make a great effort to hold a hose-pipe to throw a stream of water on fire to extinguish it. This is because the stream of water rushing through the hose-pipe in the forward direction with a large speed exerts a large force on the hose-pipe in the backward direction.

Question 9.
Why is the movement of a rocket in the upward direction?
Answer:
(i) The movement of a rocket in the upward direction can also be explained with the help of the law of conservation of momentum.

(ii) The momentum of a rocket before it is fired is zero. When the rocket is fired, gases are produced in the combustion chamber of the rocket due to the burning of fuel. These gases come out of the rear of the rocket with high speed. The direction of the momentum of the gases coming out of the rocket is in the downward direction. To conserve the momentum of the system (rocket-gases), the rocket moves upward with a momentum equal to the momentum of the gases. The rocket continues to move upward as long as the gases are ejected out of the rocket.

Question 10.
What happens when a quick jerk is given to a smooth thick cardboard placed on a tumbler with a small coin placed on the cardboard? The coin will fall in the tumbler. Why?
Answer:
The coin was initially at rest. When the cardboard moves because of the jerk, the coin tends to remain at rest due to inertia of rest. When the cardboard leaves contact with the coin, the coin falls in the tumbler on account of gravity.

Question 11.
Explain why an inflated balloon lying on the surface of a floor moves forward when pierced with a pin.
Answer:
The momentum of the inflated balloon is zero before it is pierced with a pin. Air comes out with a speed in the backward direction from balloon after it is pierced with a pin. The balloon moves in the forward direction to conserve the momentum.

Question 12.
How can force change the state of motion of the objects?
Answer:
Force can bring objects into motion by pushing, hitting and pulling them.

Question 13.
State Newton’s three laws of motion.
Answer:
Sir Isssac Newton further studied the idea of Galileo on force and motion and presented three laws of motion. These laws are as follows :
(i) First Law: A body remains in resting position or of uniform motion unless it is not introduced with an unbalanced external force.
(ii) Second Law: The rate of change of momentum of a body is directly proportional to the applied unbalanced force and change takes place in the direction of the force.
(iii) Third law: Action and reaction are equal and opposite and they act on different bodies.

Question 14.
Why is it dangerous to jump out from a moving bus?
Answer:
While moving in a bus our body is in motion. On jumping out of a moving bus our feet touches the ground and come to rest. While the upper part of our body fall in motion and moves forward due to inertia of motion and hence we can fall in forward direction. Thus, to avoid this we need to run forward in the direction of bus.

Question 15.
Give difference between balanced and imbalanced forces.
Answer:

Balanced Force	Unbalanced Force
1. Forces acting on a body from the opposite directions are same.	1. Forces acting on a body from two opposite directions are not same.
2. It does not change the state of rest or motion of an object.	2. It changes the state of rest or motion of an object.

Question 16.
Use law of conservation to explain why a gun recoils.
Answer:
Gun and bullet both are at rest before firing. Hence, their initial velocities are zero. So, the initial momentum of the gun and the bullet is zero before fire. When a bullet is fired from the gun, it moves forward with a large velocity. The bullet imparts an equal and opposite momentum to the gun due to which the gun recoils backwards. Thus, the final momentum of the system is zero.

Question 17.
Write the effect of force.
Or
What change will be in a body by force?
Answer:
Force can produce three effects :

1. It can change the magnitude of velocity of an object (i.e. to make the object move faster or slower).
2. It can change the direction of motion of an object.
3. It can change the shape and size of an object.

Question 18.
What do you understand by the gravitational unit of force?
Answer:
A gravitational unit of force is defined as that force which produces an acceleration equal to the acceleration due to gravity in a body of one unit mass.
Gram-weight and kilogram-weight are the gravitational unit of force.

Question 19.
Mention the factors on which the force of friction depends.
Answer:

• The force of friction is directly proportional to the weight of the body sliding over the surface.
• The force of friction depends on the surfaces in contact.

Question 20.
What are the disadvantages of friction?
Or
Why friction is considered wasteful?
Answer:
Friction is considered wasteful because :

• Friction leads to a loss of energy. Therefore, it reduces the efficiency of machines.
• Friction causes wear and tear of machine’s parts.

Question 21.
Name the various types of forces.
Answer:
Various types of forces are :

• Muscular force,
• Tension,
• Gravitational,
• Reaction,
• Frictional force,
• Electrical force,
• Magnetic force.

Question 22.
How is force represented graphically?
Answer:
Force is a vector quantity. So, force is represented by a line with an arrow head.

• The head of arrow represents the direction of the force.
• The length of the line is proportional to the magnitude of the force.
• This is done by choosing a convenient scale.
• For example : A force of 10 N can be represented by a line with an arrow head.
• The length of the line depends upon the scale chosen.

So, if a scale of 1 cm = 2 N is chosen, the force of 10 N is represented by a line of 5 cm in length.

Question 23.
When we hold a bag full of books in our hand steady at some height above the ground, what kind of forces are acting on it?
Answer:
The bag full of books is steady. This means its position is fixed. So, it must be under balanced forces. The forces acting on it are :

• Weight (or the gravitational pull) downwards,
• Upward force applied by the person holding the bag.

Question 24.
What happens when you shake a wet piece of cloth? Explain your observation.
Answer:
When a wet piece of cloth is shaken, small droplets of water fall down. This is because in the beginning both water and the piece of cloth were at rest. When the cloth is moved, the water in it tends to remain in the state of rest due to inertia of rest. As a result, the droplets of water fall down and the clothes dry quickly.

Question 25.
Why is it difficult to achieve a zero unbalanced force in practical situations? In practice what happens to a rolling marble? How can we reduce the effect of friction on a marble?
Answer:

• It is difficult to achieve a zero unbalanced force because of the presence of the frictional force acting opposite to the direction of motion.
• In practice, the rolling marble stops after travelling some distance.
• The effect of frictional force may be reduced by using a smoother marble and a smoother plane and providing a lubricant.

Long Answer Type Questions

Question 1.
Define force. What are different types forces?
Answer:
Force : It is a push or pull on an object that produces acceleration in the body on which it acts. The SI unit of force is Newton.

Types of forces :

• Balanced force: When the forces acting on a body from the opposite direction do not change the state of rest or of motion of an object, such forces are called balanced forces.
• Unbalanced force: When two opposite forces acting on a body move a body in the direction of the greater force or change the state of rest, such forces are called as imbalanced forces.
• Frictional force: Force of friction is the force that always opposes the motion of object.

Question 2.
What is inertia? Explain different types of inertia.
Answer:
Inertia: The natural tendency of an object to resist change in their state of rest or of motion is called inertia. The mass of an object is a measure of its inertia. Its SI unit is kg.

Types of inertia :

• Inertia of rest: The object remain in rest unless acted upon by an external unbalanced force.
• Inertia of motion: The object in the state of uniform motion will continue to remain in motion with same speed and direction unless external force is not applied on it.

Question 3.
Name three non-SI units of force. Define them.
Answer:
Some commonly used non-SI units of force are :
Dyne : The dyne is the CGS unit of force. One dyne is the force which produces an acceleration of 1 cm/s² in a body mass 1 g, i.e.
1 dyne = 1 g × 1 cm/s²
Gram-weight : It is the gravitational unit of force in CGS system. This is denoted as g-wt.
One gram weight is the force which produces an acceleration of 981 cm/s² in a body of mass 1 g. Thus,
1 g-wt = 1 g × acceleration due to gravity (g)
Or, 1 g-wt = 1 g × 981 cm/s² = 981 dynes
[∵ 1 g × 1 cm/s² = 1 dynes]
Kilogram-weight: It is the gravitational unit of force in SI system. This unit is denoted as kg-wt and it is the force which produces an acceleration of 9.81 m/s2 in a body of mass 1 kg. Thus,
1 kg-wt = 1 kg × 9.81 m/s²

Question 4.
(a) What is friction?
(b) What are the advantages of friction?
Or
Why is friction necessary?
Answer:
(a) The force which opposes the motion of one body over the surface of another is called friction or the force of friction.
(b) Friction is very desirable and an important force in our daily life. Some advantages of friction are :

• The nails and screws hold the wooden boards together due to friction.
• It is due to the friction between the ground/road and the soles of our shoes that we are able to walk.
• The friction between the road and the surface of the tyres permits safe driving.
• We are able to write on paper because of the friction between the pen/pencil and the paper. That is why, it is very difficult to write on a glazed/waxed paper.
• The application of brakes to stop a cycle, scooter or car, etc. is possible due to friction between the brake-lining and the rim of the wheel.

Question 5.
(i) What are the causes of friction?
(ii) How can friction between any two surfaces can be reduced?
Or
Describe some methods for reducing friction.
Answer:
(i) The friction rises due to the following factors :

• Due to the force of attraction between the molecules of the two surfaces in contact. This is called the force of adhesion.
• Due to the interlocking of the surface irregularities.
• Thus, friction is due to the roughness of the two surfaces in contact.

(ii) The friction between two surfaces can be reduced by following methods:

• By polishing surfaces: Rough surfaces can be made smooth by polishing. Therefore, polishing reduces friction.
• By applying oil or grease on the surfaces: Oil/grease forms a thin layer between the two surfaces and reduces friction.

Question 6.
A truck of mass M is moved under a force F. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved, then how does the acceleration change?
Answer:
Given, the initial mass m₁ = M, initial force f₁ = F
Given that, new mass m₂ = M + M = 2M and new force f₂ = F/2 (as force is halved)
From Newton’s second law,
F = ma
Therefore,
a = \(\frac{F}{m}\)
Initial acceleration (a₁) = \(\frac{F}{M}\)
New acceleration (a₂) = \(\frac{F / 2}{2 M}\)
Change in acceleration = \(\frac{a_{1}}{a_{2}}=\frac{F / M}{\frac{F / 2}{2 M}}\)
= \(\frac{F}{M} \times \frac{2 M \times 2}{F}\)
= 2M × \(\frac{2}{M}=\frac{4 M}{M}\) = 4
Therefore,
\(\frac{2}{M}=\frac{4 M}{M}\) = 4
\(\frac{a_{1}}{4}\) = a₂
Thus, the new acceleration (a₂) will be one-fourth of the old acceleration (a₁).

Question 7.
Derive a relation between force and momentum.
Answer:
Relation between force and momentum :
Let v₁ = Initial velocity of the object
Let v₂ = Final velocity of the object after time t

Now, force F = m × a
Placing the value of a,


If P₁ = mv₁ and P₂ = mv₂
then,
F = \(\frac{P_{2}-P_{1}}{t}\)
Hence, rate of change of momentum will be the force of an object.

Question 8.
Linear momentums of a car and a truck are equal. Which of these will have higher speed?
Answer:
We know that momentum of any object depends on the product of its mass and velocity.
Let the mass and velocity of car are m₁ and u₁ respectively.
∴ Momentum (P₁) = m₁v₁ ..............(i)
Similarly mass and velocity of truck are m₂ and u₂ respectively.
∴ Momentum (P₂) = m₂v₂ ..............(ii)
But, P₁ = P₂ (given)
∴ m₁v₁ = m₂v₂
or, \(\frac{m_{1}}{m_{2}}=\frac{v_{2}}{v_{1}}\)
Here \(\frac{m_{1}}{m_{2}}\) < 1, because mass of truck is greater than the mass of the car.
∴ \(\frac{v_{2}}{v_{1}}\) < 1, or v₂ < v₁
Hence speed of truck is higher than speed of car.

Solved Numericals

Question 1.
When a force of 40 N is applied on a body it moves with an acceleration of 5 m/s². Calculate the mass of the body.
Answer:
Let m be the mass of the body.
Given : F = 40 N, a = 5 m/s²
From the relation F = ma, we have 40 = m × 5
m = \(\frac{40}{5}\) = 8 kg

Question 2.
An object undergoes an acceleration of 8 ms^-2 starting from rest. Find the distance travelled in 1 second.
Answer:
Given,
Acceleration, a= 8 ms^-2
Initial velocity, u = 0
Time interval, t = 1 s
Distance travelled, s = ?
Using the equation of motion, s = ut + \(\frac{1}{2}\)at², one gets
s = 0 × 1 + \(\frac{1}{2}\) × 8 × 12 = 4m
The object travels a distance of 4 m.

Question 3.
It is required to increase the velocity of a scooter of mass 80 kg from 5 to 25 ms^-1 in 2 seconds. Calculate the force required.
Answer:
Given : m = 80 kg,
u = 5 ms^-1
v = 25 ms^-1
and t = 2 s
Now acceleration a = change in velocity time = \(\frac{v-u}{t} = \frac{25-5}{2}\) = 10 ms^-2
Force = mass × acceleration
or F = ma
Therefore, F = 80 × 10 = 800 N

Question 4.
Calculate the force required to impart to a car a velocity of 30 ms^-1 in 10 seconds. The mass of the car is 1,500 kg.
Answer:
Here u = 0 ms^-1; v = 30 ms^-1; t = 10 s; a = ?
Using v = u + at, we have
30 = 0 + a (10)
a = 3 ms^-2
Now, F = ma = 1,500 × 3
or F= 4,500 N

Question 5.
A cricket ball of mass 70 g moving with a velocity of 0.5 ms^-1 is stopped by player in 0.5 s. What is the force applied by player to stop the ball?
Answer:
Here m = 70 g = 0.070 kg; u = 0.5 ms^-1; u = 0; t = 0.5 s
F = m \(\frac{v-u}{t}\)
or, F = 0.07 \(\frac{0-0.50}{0.5}\)
or, F = -0.07 Newton
The negative sign indicates that the force exerted by the player is opposite to the direction of motion of the ball.

Question 6.
What will be acceleration of a body of mass 5 kg if a force of 200 N is applied to it?
Answer:
Here m = 5 kg; F = 200 N
F = ma or a = \(\frac{F}{m}\)
a = \(\frac{F}{m}=\frac{200}{5}\) = 40 ms^-2
a = 40 ms^-2

Question 7.
A bullet of mass 10 g is fired from a rifle. The bullet takes 0.003 s to move through its barrel and leaves with a velocity of 300 ms^-1. What is the force exerted on the bullet by the rifle?
Answer:
Here m = 10 g = 0.010 kg; u = 0; v = 300 ms^-1
t = 0.003 s, F = ?
F = \(m\left(\frac{v-u}{t}\right)\)
F = \(0.010\left(\frac{300-0}{0.003}\right)\)
F = 1,000 N

Question 8.
What force would be needed to produce an acceleration of 1 ms^-2 ball of mass 1 kg?
Answer:
Here m = 1 kg; a = 1 ms^-2; F = ?
Now F = ma = 1 × 1
or F = 1 Newton

Question 9.
What is the acceleration produced by a force of 5 N exerted on an object of mass 10 kg?
Answer:
Here F = 5 N; m = 10 kg; a = ?
Now, F = ma or a = \(\frac{F}{m}\)
a = \(\frac{5}{10}\) =0.5 ms^-2

Question 10.
How long should a force of 100 N act on a body of 20 kg so that it acquires a velocity of 100 ms^-1?
Answer:
Here v - u = 100 ms^-1, m = 20 kg; F = 100 N; t = ?
We know F = ma = \(m\left(\frac{v-u}{t}\right)\)
or, t = \(m\left(\frac{v-u}{F}\right)\)
= \(20\left(\frac{100}{100}\right)\) = 20s

Question 11.
A 1,000 kg vehicle moving with a speed of 20 ms^-1 is brought to rest in a distance of 50 m, (i) Find the acceleration; (ii) Calculate the unbalanced force acting on the vehicle; (iii) The actual force applied by the brakes may be slightly less than that calculated. Why? Give reason.
Answer:
(i) Here u = 20 ms^-1; v = 0; s = 50 m; a = ?
Using v² - u² = 2as, we have
a = \(\frac{v^{2}-u^{2}}{2 s}\)
= \(\frac{0-(20)^{2}}{2 \times 50}\)
= - 4 ms^-2
(ii) F = ma = 1,000 × (- 4) = - 4,000 N
(iii) Due to force of friction, the actual force applied by brakes may be slightly less than calculated one.

Question 12.
Which would require greater force : accelerating a 10 g mass at 5 ms^-2 or 20 g mass at 2 ms^-2?
Answer:
In first case,
m₁ = 10 g = 0.010 kg;
a₁ = 5 ms^-2 ; F₁ = ?
F₁ = m₁a₁ - 0.010 × 5
F₁ = 0.050 Newton
In second case, m₂ = 20 g = 0.020 kg
a₂ = 2 ms^-2; F₂ = ?
Now, F₂ = m₂a₂ = 0.020 × 2
or, F₂ = 0.04 Newton
We find that F₁ > F₂, hence more force is required to accelerate 10 g at 5 ms^-2 than accelerating 20g at 2 ms^-1

Question 13.
A truck starts from rest and rolls down a hill with constant acceleration. It travels a distance of 400 m in 20 s. Find itfs acceleration. Find the force acting on it if its mass is 7 metric ton.
Answer:
Here u = 0 ms^-1 (Starting from rest); s = 400 m; t = 20 s; a = ?
s = ut + \(\frac{1}{2}\) at²,
We have 400 = 0 × 20 + \(\frac{1}{2}\) × a × 20² = 200a
or a = \(\frac{400}{200}\)
a = 2 ms^-2
Now mass m = 7 metric ton = 7,000 kg; F = ?
F = ma = 7,000 × 2
or F = 14,000 N

Question 14.
A car of mass 1,000 kg moving with a velocity of 40 km h^-1 collides with a tree and comes to stop in 5 s. What will be the force exerted by car on the tree?
Answer:
Here, m = 1,000 kg
u = 40 kmh^-1 = \(\frac{100}{9}\) ms^-1
v = 0; t = 5 s
So, F = \(m\left[\frac{v-u}{t}\right]\)
F = \(\frac{1000\left(0-\frac{100}{9}\right)}{5}\)
or F = \(\frac{-20,000}{9}\)
or F = -2222 N

Question 15.
A bullet of mass 100 g is fired from a gun of mass 20 kg with a velocity of 100 ms^-1. Calculate the velocity of recoil of the gun.
Answer:
Mass of bullet, m₁ = 100 g = \(\frac{100}{1000}\) = 1 kg
Velocity of bullet, v₁ = 100 ms^-1
Mass of gun, m₂ = 20 kg
Let recoil velocity of gun = v₂
Recoil velocity of gun v₂ = \(-\frac{m_{1} v_{1}}{m_{2}}\)
= \(-\frac{1 \times 100}{20}\)
= - 0.5 ms^-1
Negative sign shows that the direction of recoil velocity of the gun is opposite to the direction of the velocity of the bullet.

Question 16.
An iron sphere of mass 10 kg is dropped from a height of 80 cm. If the downward acceleration of the ball is 10 ms^-2, calculate the momentum transferred to the ground by the ball.
Answer:
Here, initial velocity of sphere, u = 0
Distance travelled, s = 80 cm = 0.8 m
Acceleration of sphere, a = 10 ms^-2
Step 1. Final velocity of sphere when it just reaches the ground can be calculated using
v₂ - u₂ = 2as
v₂ - 0 = 2 × 10 ms^-2 × 0.8 m = 16 m²s^-2
or v = \(\sqrt{16 \mathrm{~m}^{2} \mathrm{~s}^{-2}}\) = 4 ms^-1.
Momentum of the sphere just before it touches the ground = mv = 10 kg × 4 ms^-1 = 40 kg ms^-1.

Step 2. On reaching the ground, the iron sphere comes to rest, so its final momentum = 0
According to the law of conservation of momentum,
Momentum transferred to the ground = momentum of the sphere just before it comes to rest = 40 kg ms^-1.

Question 17.
A boy of mass 60 kg running at 3 m/s jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m/s in the same direction. What is their common velocity?
Answer:
For boy, m₁ = 60 kg, u₁ = 3 ms^-1, v₁ = v
For trolley, m₂ = 140 kg, u₂ = 1.5 ms^-1, v₂ = v
By conservation of momentum,
m₁u₁ + m₂u₂ = (m₁ + m₂) v
60 × 3 + 140 × 1.5 = (60 + 140)v
v = \(\frac{180+210}{200}\)
= \(\frac{180+210}{200}\) ms^-1
= 1.95 ms^-1

Question 18.
A bullet of mass 20 g moving with a speed of 500 ms^-1 strikes a wooden block of mass 1 kg and gets embedded in it. Find the speed with which block moves along with the bullet.
Answer:
For bullet, = 20 g = 0.02 kg, u₁ = 500 ms^-1, v₁ = v
For block, m₂= 1 kg, u₂ = 0 ms^-1, v₂ = v
By conservation of momentum,
m₁u₁ + m₂u₂ = (m₁ + m₂) v
v = \(\frac{m_{1} u_{1}+m_{2} u_{2}}{m_{1}+m_{2}}\)
= \(\frac{0.02 \times 500+1 \times 0}{0.02+1}\)
= \(\frac{10}{1.02}\)
= \(\frac{1000}{102}\)
= 9.8 ms^-1

Question 19.
A force of 0.6 N acting on a body increases its velocity from 5 m/s to 6 m/s in 2 s. Calculate the mass of the body.
Answer:
F = 0.6 N, u = 5 ms^-1, v = 6 ms^-1, t = 2 s
Acceleration, a = \(\frac{v-u}{t}=\frac{6-5}{2}=\frac{1}{2}\) ms^-2 = 0.5 ms^-2
m = \(\frac{F}{a}=\frac{0.6}{0.5}\) = 1.2 mg