These AP 9th Class Physics Important Questions 8th Lesson Force and Laws of Motion will help students prepare well for the exams.

## AP 9th Class Physics 8th Lesson Force and Laws of Motion Important Questions

### Class 9 Physical Science Chapter 8 Important Questions – 2 Marks

Question 1.

What happens when we ride a bicycle and stop pedalling ? Why ?

Answer:

- When, we stop pedalling, the bicycle begins to slow down.
- This is again because of the friction forces acting opposite to the direction of motion.

Question 2.

What type of forces are required to move an object with

a) a uniform velocity

b) acceleration?

Answer:

a) A balanced force is required to maintain a uniform velocity.

b) An unbalanced force is required to move with acceleration.

Question 3.

How do safety belts work to prevent injury in a car accident?

Answer:

- Safety belts exert a force on the passenger’s body to slow down their forward motion when the car suddenly stops due to braking.
- This helps to prevent injury or collision with the car’s panels in front by reducing the passenger’s speed and bringing them to a stop along with the car

Question 4.

What happens when the ball is released from the left top of an inclined plane as shown in the figure?

Answer:

When the marble is released from left, it would roll down the slope and go upon the opposite side to the same height from which it was released.

Question 5.

What happens when the ball is released from the left top of an inclined plane as shown in the adjacent figure (assume that it is a frictionless plane)?

Answer:

The marble would continue to travel forever trying to reach the same height that it was released from.

Question 6.

What is the explanation for why we get thrown to one side when a motorcar makes a sharp turn at high speed?

Answer:

- The law of inertia explains why we get thrown to one side when a motorcar makes a sharp turn at high speed.
- Our body tends to continue in its straight-line motion and when an unbalanced force is applied by the engine to change the direction of motion of the motorcar, we slip to one side of the seat due to the inertia of our body.

Question 7.

Do all bodies have the same inertia? Explain with an example.

Answer:

- Heavier or more massive objects offer larger inertia Quantitatively, the inertia of an object is measured by its mass.
- A force that is just enough to cause a small cart to pick up a large velocity will produce a negligible change in the motIon of a train.
- The train has more Inertia than the cart.
- Hence, ail bodies do not have the same inertiAnswer:

Question 8.

What do you observe lnead of a five-rupee coin If we ie a one-rupee coin In the activity given In the figure?

Answer:

In the activity given in the figure. instead of a five-rupee coin If we use a one-rupee coin, we find that a lesser force is required to perform the activity.

Question 9.

Compare inertia and mass.

Answer:

- Inertia is the natural tendency of an object to resist a change in its state of motion
- The mass of an object is a measure of its inertia.

Question 10.

What is the second law of motion ?

Answer:

- The second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.
- In other words, the force required to change the momentum of an object depends on the rate at which the momentum is changed.

Question 11.

Write the relation between force and acceleration. What are the units of force ?

Answer:

- The relation between force and acceleration is F = ma.
- The unit of force is kg ms
^{-2}or newton (N).

Question 12.

High jump athletes use a cushioned bed to fall. Why ?

Answer:

- In a high jump athletic event, the athletes are made to fall either on a cushioned bed or on a sand bed.
- This is 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 13.

How a karate player breaks a slab of ice with a single blow ?

Answer:

- When a karate player strikes a slab of ice with a single blow, they transfer their momentum to the ice, causing it to break.
- Momentum is a product of an object’s mass and velocity and the faster and more massive the strike, the greater the momentum transferred to the ice, resulting in a more forceful and effective break.

Question 14.

What is the alternative statement of the third law of motion ? Give an example.

Answer:

- The alternative statement of the third law of motion is “to every action there is an equal and opposite reaction.”
- Eg: Launching a rocket is working on the third law of motion.

Question 15.

What is an example of the first law of motion in daily life ?

Answer:

An example of the first law of motion in daily life is when a person in a moving car suddenly stops, their body continues to move forward until they are stopped by the seatbelt or another object.

Question 16.

What is an example of the third law of motion in daily life ?

Answer:

An example of the third law of motion in daily life is when a person jumps off a diving board into a swimming pool. As they push down on the diving board, the board pushes back on them with an equal and opposite force, propelling them upwards.

Question 17.

What are the action and reaction forces acting on the gun while firing ?

Answer:

- A forward force on the bullet (action).
- Recoil force on the gun (reaction).

Question 18.

A 10 kg block is pulled along a frictionless surface by a force of 20 N. What is the acceleration of the block ?

Answer:

Given, m = 10 kg; F = 20 N

According to the second law of motion, F = ma; a = F/m = 20 N / 10 kg = 2m/s^{2}

Therefore, the acceleration of the block is 2 m/s^{2}.

Question 19.

A 2kg object is moving with a velocity of 5 m/s. What is its momentum ?

Answer:

Momentum (P) = mass (m) × velocity (v)

P = 2 kg × 5 m/s = lu kg m/s

Therefore, the momentum of the object is 10 kg m/s.

Question 20.

An object has a momentum of 25 kg m/s and a mass of 5 kg. What is its velocity ?

Answer:

Momentum (P) = mass (m) × velocity (v)

Rearranging the formula, we get velocity (v) = momentum (P) / mass (m)

v = 25 kg m/s / 5 kg = 5 m/s

Therefore, the velocity of the object is 5 m/s.

Question 21.

Write the effects of force.

Answer:

- A force or set of forces, can bring the object into motion.
- Forces can bring the object to rest.
- Forces can change the direction of motion of the particle.
- Forces can change the shape of particle.

Question 22.

Write the types of Inertia.

1) Inertia of rest

2) Inertia of motion

3) Inertia of direction

Answer:

1) Inertia of rest : State where particle (or) body continuous to remain in rest.

Ex : Mountain Rocks.

2) Inertia of motion : State where moving body keeps moving without any change of velocity.

Ex : Rotation of fan.

3) Inertia of direction : State where moving body continues to be maintaining same direction (Rectilinear).

Question 23.

How inertia & mass related to each other ?

Answer:

- Inertia of an object is measured by mass.
- Inertia & mass are directly proportional to each other.

Inertia ∝ mass - Heavier bodies have greater Inertia.
- Mass of an object is measure of Inertia.

Question 24.

Define 1 Newton.

Answer:

If a force acting on a body of mass 1kg produces an acceleration of 1ms^{-2} in it the force is said to be 1 Newton.

F = 1 Newton ; m = 1kg ; a = 1 ms^{-2}; k = 1

F = kma

I N = 1 × 1kg × 1 ms^{-2} = 1 kgms^{-2}

Note : The net force acting on a particle is equal to change of momentum.

Question 25.

State Newton’s third law.

Answer:

When one object exerts a force on another object, the second object instantaneously exert a force back on first.

In short : To Every action there is equal and opposite reaction.

Note : Any pair of equal and opposite forces are not action – reaction pair.

Question 26.

How does the second law of motion relate to momentum and force ?

Answer:

The second law of motion relates the rate of change of momentum to the applied unbalanced force. In other words, the greater the force applied, the greater the rate of change of momentum.

Question 27.

What is the third law of motion ?

Answer:

The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction.

Question 28.

A vehicle of mass 300 kg travels at a velocity of 90 km/h. Find its momentum.

Answer:

Mass of the vehicle (m) = 300 kg

Velocity of the vehicle (v) = 90 km/h = 90 × \(\frac{5}{18}\) m/s = 25 m/s

Momentum = mv = 300 × 25 = 7500 kg.m.s^{-1}

Question 29.

“With our day to day experience, we must exert some force on an object to keep it moving”.

i) By which law, you can support the above lines ?

ii) Which act oh the body ? Either force or net force ?

Answer:

i) Newtons first law of motion.

ii) Net force. The position of object is changed due to net force only.

Question 30.

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-rupee coin.

Answer:

As the mass of the object increases the inertia of the object increases.

a) Stone has more mass than rubber ball. So stone has more inertia.

b) Train has more inertia.

c) 5 rupee coin has more inertia.

Question 31.

Why does a person in a bus tend to fall forward, when it stops suddenly ?

Answer:

When the driver of a bus in which a person is travelling applies brakes suddenly, the person tends to move forward due to inertia.

Question 32.

Give one point of difference between balanced and unbalanced forces.

Answer:

- When forces acting on a body from all sides are equal, they cancel effect of each other and are known as balanced forces.
- When forces acting on a body are not equal are called unbalanced forces.

Question 33.

State three characteristics of action – reaction forces.

Answer:

- Equal in magnitude,
- Opposite in direction,
- Acts simultaneously on 2 different bodies.

Question 34.

A body of mass 1 kg is kept at rest. A constant force of 6N starts acting on it. Find the time taken by the body to move through a distance of 12m.

Solution:

m = 1kg; u = 0; F = 6N; s = 12m ; t = ?; F = ma .

a = \(\frac{\mathrm{F}}{\mathrm{~m}}\) = \(\frac{6}{1}\) = 6 m/s^{2}

s = ut + 1/2 at^{2}

12 = 0 × t + 1/2 × 6 × t^{2} ⇒ 3t^{2} = 12 ⇒ t^{2} = 4 ⇒ t = 2s

Question 35.

Write an activity to show that inertia of a body depends on its mass.

Answer:

- Apply some force on a football.
- It flies away as it has small inertia.
- Apply same force on same size of stone,
- Stone hardly moves as it has more inertia.

Question 36.

State the law of inertia.

Answer:

An object remains in its state of rest or of uniform motion in a straight line until an external unbalanced force acts on it.

Question 37.

A girl of mass 50 kg jumps out of a moving boat of mass 300 kg on to the bank with a horizontal velocity of 3 m/s. With what velocity does the boat begin to move backwards?

Solution:

m_{1} = 50 kg; m_{2} = 300 kg; u_{1} = 3 m/s ; u_{2} = ?

m_{1}u_{1} + m_{2}u_{2} = 0

u_{2} = \(\frac{-m_1 u_1}{m_2}\)

### Force and Laws of Motion Class 9 Important Questions – 3 Marks

Question 1.

Write three laws of motion.

Answer:

- First law of motion : An object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force.
- Second law of motion : The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.
- Third law of motion : To every action, there is an equal and opposite reaction and they act on two different bodies.

Question 2.

Define

i) inertia

ii) mass

iii) force

iv) momentum.

Answer:

i) Inertia : The natural tendency of objects to resist a change in their state of rest or of uniform motion is called inertia.

ii) Mass : The mass of an object is a measure of its inertia. Its S.I. unit is kilogram (kg).

iii) Force : Force of friction always opposes motion of objects.

The S.I. unit of force is kg ms^{-2}.

This is also known as newton and represented by the symbol N.

iv) Momentum : The momentum of an object is the product of its mass and velocity and has the same direction as that of the velocity. Its S.I. unit is kg ms^{-1}.

Question 3.

When does an object maintain uniform velocity ?

(OR)

“An object maintains its motion under the continuous application of an unbalanced force.” Is it the correct statement?

Answer:

- An object maintains its motion under the continuous application of an unbalanced force. It is quite incorrect.
- An object moves with a uniform velocity when the forces (pushing force and frictional force) acting on the object are balanced and there is no net external forefe on it.
- If an unbalanced force is applied on the object, there will be a change either in its speed or in the direction of its motion.

Question 4.

Why is the first law of motion also calling the law of inertia ?

Answer:

- The first law of motion is stated as an object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force.
- In other words, all objects resist a change in their state of motion. In a qualitative way, the tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia.
- This is why, the first law of motion is also known as the law of inertia.

Question 5.

Explain the concept of inertia and how it is related to motorcar accidents.

Answer:

- Inertia is the tendency of an object to resist any change in its state of motion.
- When travelling in a motorcar, our body tends to remain at rest with respect to the seat until the driver applies a braking force to stop the car.
- With the application of brakes, the car slows down but our body tends to continue in the same state of motion because of its inertia.
- A sudden application of brakes may cause injury to us by impact or collision with the panels in front.

Question 6.

Why do passengers tend to fall backward when a bus starts suddenly ?

Answer:

- When standing in a bus and the bus begins to move suddenly, our feet in contact with the floor of the bus gain motion along with the bus.
- However, the rest of our body opposes this motion due to its inertia.
- As a result, we tend to fall backward.
- This is because our body is trying to remain in its state of rest while our feet are moving forward with the bus.

Question 7.

What is momentum ? Is it scalar or vector ? What are its units ? Which one can change the momentum of an object ?

Answer:

- The momentum, P of an object is defined as the product of its mass m and velocity, v.

That is, P = mv. - Momentum has both direction and magnitude. Its direction is the same as that of velocity, v. Hence it is a vector.
- The S.I. unit of momentum is kilogram-metre per second (kg m s
^{-1}) - Since the application of an unbalanced force brings a change in the velocity of the object, it is therefore clear that a force also produces a change of momentum.

Question 8.

Explain the concept of action and reaction forces with an example.

Answer:

- According to the third law of motion, when one object exerts a force on another object, the second object instantaneously exerts a force back on the first.
- These two forces are always equal in magnitude but opposite in direction.
- For example, when a gun is fired, it exerts a forward force on the bullet. The bullet exerts an equal and opposite force on the gun, resulting in the recoil of the gun.
- Similarly, when a person intends to start walking on a road, they push the road below backwards and the road exerts an equal and opposite force on their feet to make them move forward.

Question 9.

Explain how walking is possible on the road regarding the third law of motion.

(OR)

What force is required to accelerate from a state of rest when walking on a road and in what direction does this force act ?

Answer:

- Suppose you are standing at rest and intend to start walking on a road.
- You must accelerate and this requires force in accordance with the second law of motion.
- You push the road below backward.
- The road exerts an equal and opposite force on your feet to make you move forward.

Question 10.

How force and period of application of force (time – period) related with each other ?

Answer:

Second law – sports :

- In cricket it is easy to catch a fast moving ball by pulling back your arm.
- This allows to apply a small force on hands as you have more time.
- If you try to catch the ball without moving your arms backwards.
- Greater force is required in a very short interval to catch the ball.
- This may hurt the fielder or catch may be dropped.

Therefore, force &time period are related with each other.

Question 11.

Why we have to wear a seat belt while driving a car ?

Answer:

- While travelling in a car we are at rest with respect to seat and in motion with respect to car.
- When the brakes are applied suddenly the car comes to rest but we tend to continue in motion due to inertia of motion.
- This may cause injury to us.
- Seat belt exert a force and slows down our forward movement.

Note : Momentum had both magnitude and direction, so it is a vector quantity.

Question 12.

Give daily life examples of momentum.

Answer:

- During the game of table-tennis if the ball hits a player it does not hurt him. On the other hand^ when a fast-moving cricket ball hits a spectator, it may hurt him.
- A truck at rest does not require any attention when parked along a roadside. But a moving truck, even at speeds as low as 5 ms
^{-1}, may kill a person standing in its path. - A small mass, such as a bullet may kill a person when fired from a gun.
- These observations suggest that the impact produced by the objects depends on their mass and velocity. That means momentum.

Question 13.

Give some examples for Newton’s third law of motion from your day to day observations.

Answer:

1) Flying of birds:

a) When birds fly, they push the air downward with their wings.

b) The air pushes back the bird in opposite upward direction.

c) These two forces are equal in magnitude and opposite in direction. Hence the bird can fly.

2) Swimming of fish :

a) When a fish swims in water, it pushes back the water.

b) The water pushes the fish with equal but in opposite direction.

c) Hence the fish moves forward.

3) Launching of a rocket:

a) A rocket accelerates by expelling gas at high velocity.

b) The reaction force of the gas on the rocket accelerates the rocket in a direction opposite to the expelled gases.

Question 14.

From a fixed height, two eggs are dropped such that one fails on a concrete floor and the other on a cushioned pillow. The egg falling on the concrete floor breaks and the one foiling on the pillow does not break. Explain why in terms of momentum.

Answer:

- The change of momentum of an egg takes place in shorter time in case of concrete surface.
- The change of momentum of the egg takes place in longer time in case of cushioned pillow.
- Hence, egg does not break on cushioned pillow.

Question 15.

Two objects having their masses in ratio 3 : 5 are acted upon by two forces each one object. The forces are in the ratio of 5 : 3. Find the ratio in their accelerations.

Answer:

Since masses are in ratio 3 : 5.

Let the mass of the object be 3x and 5x.

Let F_{1} & F_{2} be the two forces a_{1} and a_{2} accelerations.

F_{1} = m_{1}a_{1} = 3xa_{1} ; F_{2} = m_{2}a_{2} = 5xa_{2}

F_{1} : F_{2} = 5 : 3 ⇒ 3xa_{1} : 5xa_{2} = 5 : 3

a_{1} : a_{2} = 5 × 5 : 3 × 3 ⇒ a_{1} : a_{2} = 25 : 9

Question 16.

A scooter is moving with a velocity of 25 m/s and it takes 5s to stop after the brakes are applied. If the mass of the scooter along with the rider is 180 kg, find the change in momentum in this case.

Answer:

u = 25m/s ; v = 0 ; t = 5s ; m = 180kg

P_{i} = mu = 180 × 25 = 4500 kg m/s ; P_{f} = mv = 180 × 0 = 0 kg m/s

P_{f} – P_{i} = 0 – 4500 = -4500 kg m/s

Question 17.

a) Newton’s first law of motion is also called law of inertia. Justify the statement.

b) A plastic ball & a cricket ball are rolled on the floor with same velocity which one will cover larger distance before stopping ?

c) A truck is moving with a velocity of 72 km/h and it takes 3s to stop after the brakes are applied. Calculate the force exerted by brakes. Mass of truck is 1200kg.

Answer:

a) Everybody tends to resist change of state whether of rest or of motion.

b) Cricket ball.

c) u = 72 km/h = 20 m/s ; v = 0 ; t = 3s ; m = 1200 kg

v = u + at ⇒ a = \(\frac{v-u}{t}\) = \(\frac{-20}{3}\) = – 6.6 m/s^{2}

F = ma = 1200 × -6.6 =-7920N

Question 18.

a) State the law that provides, the formula for measuring force & the law which provides the definition of force.

b) Velocity – time graph of a 50g marble rolling on floor is given below. Find

i) Time in which it stops.

ii) – ve acceleration produced on it.

iii) + ve force acting on the marble

Answer:

a) 2^{nd} law of motion gives us a method to measure the force acting on an object as force is the product of its mass and acceleration.

b) i) t = 25 s

ii) a = \(\frac{30 – 0}{25}\) = 1.2 m/s^{2}

iii) F = ma = (\(\frac{50}{1000}\)) × 1.2 = 0.06N

Question 19.

a) Define momentum. Write its S.I. unit.

b) How much momentum will an object of mass 10kg transfer to the floor, if it foils from a height of 5m ?

Answer:

a) Momentum is the product of mass and velocity; S.I. unit – kgm/s

b) v^{2} = u^{2} + 2gh

v^{2} = (0)^{2} + 2(10)(5) ⇒ v^{2} = 100 ⇒ v = 10 m/s

P = mv = 10 × 10 = 100 kgm/s

Question 20.

a) When a bullet is fired from a gun, the gun moves backward. Give reason.

b) A gun of mass 500g fires a bullet of mass 10g with a speed of 100 m/s. Find.

i) Initial momentum of ‘gun + bullet’.

ii) Momentum gained by the bullet after firing,

iii) Recoil velocity of the gun.

Answer:

a) Gun exerts force on bullet in forward direction. In turn bullet also exerts an equal and opposite force in backward direction.

b) i) Zero

ii) m_{1}v_{1} = 10/1000 × 100 = 1 × kgm/s

iii) m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

0 = 1 + (\(\frac{500}{1000}\)) v_{2} ⇒ v_{2} = -2 m/s

Question 21.

Two objects of masses 100g and 200g are moving along the same line and direction with velocities of 2 m/s and 1 m/s. They collide and after the collision, the first object moves at a velocity of 1.67 m/s. Find the velocity of second object.

Solution:

m_{1} = 100 g = 0.1 kg ; m_{2} = 200 g = 0.2 kg ; u_{1} = 2 m/s ; u_{2} = 1m/s

v_{1} = 1.67 m/s ; v_{2} = ?

m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

0.1 × 2 + 0.2 × 1 = 0.1 × 1.67 + 0.2 × v_{2}

0.2 + 0.2 = 0.167 + 0.2 v_{2}

v_{2} = 1.165 m/s

### Important Questions on Force and Laws of Motion Class 9 – 5 Marks

Question 1.

How do you prove that an unbalanced force acting on an object brings it in motion?

(OR)

How do you demonstrate balanced and unbalanced forces through an activity ?

Answer:

- Place a wooden block on a horizontal table.
- Take two strings X and Y tied to the block’s two opposite faces.
- If we apply a force by pulling the string X, the block begins to move to the right.
- Similarly, if we pull the string Y, the block moves to the left.
- But, if the block is pulled from both the sides with equal forces, the block will not move.
- Such forces are called balanced forces and do not change the state of rest or of motion of an object.
- Now, let us consider a situation in which two opposite forces of different magnitudes pull the block.
- In this case, the block would begin to move in the direction of the greater force.
- Thus, the two forces are not balanced and the unbalanced force acts in the direction the block moves.
- This suggests that an unbalanced force acting on an object brings it in motion.

Question 2.

What happens when some children try to push a box on a rough floor with a small force ? What to do to move the box ? Why ?

Answer:

- The box does not move because of friction acting in a direction opposite to the push. (fig. (a))
- This friction force arises between two surfaces in contact; in this case, between the bottom of the box and the floor’s rough surface.
- It balances the pushing force and therefore the box does not move.
- In Fig. (b), the children push the box harder but the box still does not more. This is because the friction force still balances the pushing force.
- If the children push the box harder still, the pushing force becomes bigger than the friction force [Fig. (c)].
- There is an unbalanced force.
- So, the box starts moving.

Question 3.

Explain the Galileo experiment of marble on an inclined plane.

Answer:

- The fig. shows the inclined plane and a marble.
- Galileo argued that when the marble is released from the left, it would roll down the slope and go upon the opposite side to the same height from which it was released.
- If the inclinations of the planes on both sides are equal, then the marble will climb the same distance that it covered while rolling down.
- If the angle of inclination of the right-side plane were gradually decreased, then the marble would travel further distances till it reaches the original height.
- If the right-side plane were ultimately made horizontal (that is, the slope is reduced to zero), the marble would continue to travel forever trying to reach the same height that it was released from.
- The unbalanced forces on the marble in this case are zero.
- It thus suggests that an unbalanced (external) force is required to change the motion of the marble but no net force is needed to sustain the uniform motion of the marble.
- In practical situations it is difficult to achieve a zero unbalanced force.
- This is because of the presence of the frictional force acting opposite to the direction of motion. Thus, in practice, the marble stops after travelling some distance.
- The effect of the frictional force may be minimized by vising a smooth marble and a > smooth plane and providing a lubricant on top of the planes.

Question 4.

Write three laws of motion with examples.

Answer:

1) Newton’s First Law of Motion : Law of Inertia

An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

Example : A soccer ball sitting on a field will remain still until someone kicks it, causing it to move.

2) Newton’s Second Law of Motion : Law of Acceleration

The acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.

Example : A small car and a large truck both accelerate at the same rate when the same force is applied to both, but the larger truck requires more force to accelerate than the smaller car.

3) Newton’s Third Law of Motion : Law of Action and Reaction

For every action, there is an equal and opposite reaction.

Example : When a person jumps off a diving board, they push down on the board with a force that is equal and opposite to the force that propels them upwards.

Question 5.

Derive F = ma.

(OR)

Derive a relation between forces applied on an object and its acceleration.

(OR)

Express Newton’s second law of motion with a mathematical formula.

Answer:

Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t. The initial and final momentum of the object will be, P_{1} = mu and P_{2} = mv respectively.

The change in momentum ∝ P_{2} – P_{1}

∝ mv – mu ⇒ ∝ m × (v – u)

The rate of change of momentum ∝ \(\frac{\mathrm{m} \times(\mathrm{v}-\mathrm{u})}{\mathrm{t}}\)

(or) the applied force, F ∝ \(\frac{\mathrm{m} \times(\mathrm{v}-\mathrm{u})}{\mathrm{t}}\) ⇒ F = \(\frac{\mathrm{km} \times(\mathrm{v}-\mathrm{u})}{\mathrm{t}}\) = kma

Here a [ = (v – u)/t ] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality. The S.I. units of mass and acceleration are kg and ms^{-2} respectively. The unit of force is so chosen that the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produces, an acceleration of 1 ms^{-2} in an object of 1 kg mass. That is,

1 unit of force = k × (1 kg) × (1 ms^{-2}).

Thus, the value of k becomes 1. From Eq. F = ma

Question 6.

Derive mathematic formulae of Newton’s second law of motion.

Answer:

The rate of change of momentum of a particle (body) is proportional to the net force acting on it. –

- Suppose an object (particle) of mass = m
- Moving along straight line with an initial velocity = u
- It accelerated uniformly and attained a velocity = v

at :

- Time interval = t
- Then initial momentum of particle is P
_{1}= mu - Final momentum of particle is P
_{2}= mv

Rate of :

- Change of momentum ∝ \(\frac{P_2-P_1}{t}\) ∝ \(\frac{m v-m u}{t}\) ∝ \(\frac{m(v-u)}{t}\)
- Change of momentum is Forcce F ∝ \(\frac{m(v-u)}{t}\)

From kinematics, v = u + at

v – u = at a = \(\frac{v-u}{t}\) ………….. (1)]

F ma [from (1)]

F = kma [where k is proportionality constant whose value k = 1]

Question 7.

State and prove principle of conservation of linear momentum.

If the net external force on a system of particles is zero, the linear momentum of the system remains constant.

Proof :

Case I) :

- Suppose two balls A & B of masses m
_{1}& m_{2}travelling in the same direction along straight line. - Initial velocity of Ball A = u
_{1} - Initial velocity of Ball B = u
_{2}[u_{1}> u_{2}] - Initial momentum of Ball A(P
_{A}) = m_{1}u_{1} - Initial momentum of Ball B(P
_{B}) = m_{2}u_{2} - Total momentum of Balls A & B = P
_{A}+ P_{B}

P_{1}= m_{1}u_{1}+ m_{2}u_{2}

Case ii) :

Ball A will collide with Ball B at some time [u_{1} > u_{2}] “t”.

- Ball A exert a force F on Ball B.
- Ball B exert a force – F on Ball A.

Case iii) :

After collision Ball A & Ball B separate.

- Final velocity of Ball A = v
_{1} - Final velocity of Ball B = v
_{2}

Force = F acting on A (due to B)

∴ Momentum before collision = Momentum after collision

So, the total momentum of the system remains constant.

∴ Momentum is conserved.

Question 8.

Which is having higher value of momentum ?

Answer:

bullet of mass 1 Og moving with a velocity of 400m/s or a cricket ball of mass 400g thrown with the speed of 90 Km/hr.

Answer:

P = m × v

Mass of bullet = 10g = 10 × 10^{-3} kg = 10^{-2} kg

Velocity of bullet = 400 m/s

Momentum of bullet = 10^{-2} kg × 400 m/s = 4 kg m/s

Mass of cricket ball = 400g = 400 × 10^{-3} kg = 0.400 kg

Velocity of ball = 90 km/hr = 90 × \(\frac{1000 \mathrm{~m}}{3600 \mathrm{~s}}\) = 25 m/s

Momentum of ball = 0.400 × 25 = 10 kg m/s

∴ The cricket ball has higher momentum.

Question 9.

How would you arrive at a mathematical formula to measure force using second law of motion ? Define the unit of force using this formula.

Answer:

Initial momentum = P_{1} = mu ; Final momentum = P_{2} = mv

Change in momentum = P_{2} – P_{1} = mv – mu = m(v – u)

F ∝ \(\frac{P_2-P_1}{t}\) ⇒ F ∝ \(\frac{m(v-u)}{t}\) ⇒ F ∝ ma ⇒ F = kma ⇒ F = ma [∵ k = 1 ]

### Extra Questions on Force and Laws of Motion Class 9 – 4 Marks

I. Look at the diagram below and answer the following questions:

a) What can be measured by using spring balance ?

Answer:

Force.

b) What is the force applied on B if force applied on A is 20 N ?

Answer:

20 N.

c) What type of forces these two represent ?

Answer:

Action & Reaction.

d) Does any pair of opposite force are action & reaction forces ?

Answer:

No.

II. A girl of mass 40 kg jumps with a horizontal velocity of 5 ms^{-1} onto a stationery cart with frictionless wheels. The mass of the cart is 3 kg. Based on the given information answer the following questions.

a) What is the initial momentum of girl ?

Answer:

200 N (or) kg ms^{-1}.

b) What is the initial momentum of cart ?

Answer:

0.

c) What is the total momentum when the girl jump on cart ?

Answer:

43 kgms^{-1}.

d) What is the velocity as the cart starts moving ?

Answer:

4.65 ms.

III. Two hockey players of opposite teams, while trying to hit a hockey ball on the ground collided and immediately become entangled one has a mass of 60 kg and was moving with a velocity 5.0 ms^{-1} while the other has a mass of 55 kg and was moving faster with a velocity of 6.0 ms^{-1} towards first player. Based on the above information answer the following questions.

a) Find the initial momentum of player I.

Answer:

300 kg ms^{-1}

b) Find the initial momentum of player II.

Answer:

330 kgms^{-1}

c) What is the total momentum of two players hefore collision ?

Answer:

– 30 kgms^{-1}

d) With what velocity they will move after they entangled ?

Answer:

– 0.26 ms^{-1}