Science Chapter 2 - Force And Laws Of Motion

Answer:

The product of mass and velocity of a body is called momentum.

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Momentum is the physical quantity which is considered to be a measure of the quantity of motion of a body.

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The SI unit of momentum is kilogram meter per second (kg.m/s).

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Momentum is a vector quantity.

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The total momentum of the bullet and gun before it is fired  is zero.

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Momentum is the physical quantity whose unit is kg.m/s.

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Momentum of a body of mass 'm' moving with a velocity 'v' =  m × v

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Balanced forces are the forces which cannot produce motion in a body but can change its shape.

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Friction is the unbalanced force which slows down a moving bicycle when we stop pedalling it.

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False, unbalanced forces acting on a body changes its speed or its direction of motion, but does not change its shape.

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Gravity is the force which causes this change in the speed of the ball.

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The property of bodies to resist a change in their state of rest or of motion is called inertia.

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‘Galileo’s law of inertia’ is the other name for Newton’s first law of motion.

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Object B has more inertia because heavier objects have greater inertia than lighter objects.

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Sir Isaac Newton gave the laws of motion.

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Force is a vector quantity.

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The speed of a running bull should be multiplied by the mass (of the bull) so as to obtain its momentum.

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(a) Mass is a measure of the inertia of a body.
(b) When a running car stops suddenly, the passengers are jerked forward.
(c) When a stationary car starts suddenly, the passengers are jerked backward
(d) Newton’s first law of motion is also called Galileo’s law of inertia.
(e) If there were no unbalanced force of friction and no air resistance, a moving bicycle would go on moving forever.

Answer:

It is easier to stop a tennis ball than a cricket ball moving with the same speed because it has less momentum than the cricket ball.

Answer:

The given equation describes the momentum of a body as the product of its mass and velocity.
P = m × v
where, P = momentum
m = mass of the body
v = velocity of the body

Answer:

A Karate player can break a pile of tiles with a single blow of his hand. This is because he strikes the piles of tiles with very fast motion of his hand. In doing so, large momentum of the fast moving hand is almost reduced to zero in a very short time. This exerts a very large force on the pile of tiles which is sufficient to break them apart.

Answer:

We know that:
Momentum = mass × velocity
                   = m × v
Here, mass, m = 200 g  
or m = 0.2 kg
And, velocity, v = 5 m/s
Putting these values in the above formula, we get:
Momentum = 0.2 × 5 kg.m/s = 1 kg.m/s.

Answer:

We know that:
Momentum = mass × velocity
                    = m × v
Here, mass, m = 1500 kg
And, velocity, v = 36 km/h
$$\begin{gathered} =36\times \frac{1000}{3600} \\ =36\times \frac{10\cancel{00}}{36\cancel{00}} \\ =\cancel{36}\times \frac{10}{\cancel{36}} \\ =10 \mathrm{m}/\mathrm{s} \end{gathered}$$

Putting these values in the above formula, we get:
Initial Momentum = 1500 × 10  kg.m/s = 15000 kg.m/s

Also, we know that:
Momentum = mass × velocity
                    = m × v
Here, mass, m = 1500 kg
And, velocity, v = 72 km/h
$$\begin{gathered} =72\times \frac{1000}{3600} \\ =72\times \frac{10\cancel{00}}{36\cancel{00}} \\ ={\cancel{72}}^2\times \frac{10}{\cancel{36}} \\ =20 \mathrm{m}/\mathrm{s} \end{gathered}$$
Putting these values in the above formula, we get:
Final Momentum = 1500 × 20 kg.m/s = 30000 kg.m/s.

The change in momentum of a car weighing 1500 kg when its speed increases from 36 km/h to 72 km/h = 30000 kg.m/s − 15000 kg.m/s = 15000 kg.m/s.

Answer:

We know that:
Momentum = mass × velocity
                   = m × v
Here, mass, m = 25 kg
And, momentum = 125 kg.m/s
Putting these values in the above formula, we get:
125 kg.m/s = 25 × velocity
$$\begin{gathered} \Rightarrow \mathrm{Velocity}=\frac{125}{25} \\ \Rightarrow \mathrm{Velocity}=\frac{{\cancel{125}}^5}{\cancel{25}} \\ \Rightarrow \mathrm{Velocity}=5 \mathrm{m}/\mathrm{s} \end{gathered}$$

Answer:

(a) We know that:
Momentum = mass × velocity
                   = m × v
Here, mass, m = 2000 kg
velocity, v = 5 m/s
Putting these values in the above formula, we get:
Momentum = 2000 × 5 kg.m/s = 10000 kg.m/s

(b) We know that:
Momentum = mass × velocity
                   = m × v
Here, mass, m = 0.02 kg
And, velocity, v = 400 m/s
Putting these values in the above formula, we get:
Momentum = 0.02 × 400 kg.m/s = 8 kg.m/s

Answer:

Balanced forces can change the shape of an object.
For example, on pressing a rubber ball between our hands, the shape of the rubber ball changes from spherical to oblong.

Answer:

The tendency of a body to remain at rest (stationary) or in uniform motion is called inertia. It is the property of a body to resist a change in its state of motion or of rest.

Answer:

According to Newton’s first law of motion:
A body at rest will remain at rest and a body in motion will continue in motion in a straight line with a constant velocity, unless it is compelled by an external force to change its state of rest or of uniform motion.

Examples:
(a) A book lying on a table cannot change its state of rest unless an external force is applied on the book.
(b) A car set free on a sloppy road will continue to be in motion unless an external force applied by hands or brakes to bring the car to rest.

Answer:

The inertia of a body depends on its mass.    
A cricket ball has more inertia than a rubber ball of the same size because it has more mass than a rubber ball.

Answer:

When a bus starts suddenly, the passengers tend to jerk backward. This is because their bodies possess inertia due to which the passengers tend to remain in their state of rest (or stationary state) even when the bus has started moving.

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When a moving bus stops suddenly, the passengers are jerked forward because of inertia. The passengers tend to remain in their state of motion (which they possess in a moving bus) even though the bus has come to rest.

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When a hanging carpet is beaten with a stick, the dust particles come out of it because the force of the stick makes the carpet move to-and-fro slightly but the dust particles tend to remain at rest (or stationary) due to their inertia and hence get separated from the carpet.

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When a tree (having flexible stems) is shaken vigorously, its fruits and leaves fall down. This is due to the fact that when the tree is shaken, it moves to-and-fro slightly but its fruits and leaves tend to remain at rest (or stationary) due to their inertia. Thus, they get detached from the tree and fall down.

Answer:

It is dangerous to jump out of a moving bus because the person who jumps is moving with the same speed as that of the bus and would tend to remain in motion (due to inertia) even after falling to the ground; thus, he may get hurt due to the resistance of the stationary ground.

Answer:

(a) 5 m/s
We know that:
Momentum = mass × velocity
                   = m × v
Here, mass, m = 10 kg
velocity, v = 5 m/s
Putting these values in the above formula, we get:
Momentum = 10 × 5 kg.m/s
                   = 50 kg.m/s
 
(b) 20 cm/s
We know that:
Momentum = mass × velocity
                   = m × v
Here, mass, m = 10 kg
velocity, v = 20 cm/s
v = 0.2 m/s
Putting these values in the above formula, we get:
Momentum = (10)(0.2) kg.m/s
                   = 2 kg.m/s

(c) 36 km/h
We know that:
Momentum = mass × velocity
                   = m × v
Here, mass, m = 10 kg
velocity, v = 36 km/h
                $$\begin{gathered} =36\times \frac{1000}{3600} \\ =36\times \frac{10\cancel{00}}{36\cancel{00}} \\ =\cancel{36}\times \frac{10}{\cancel{36}} \\ =10 \mathrm{m}/\mathrm{s} \end{gathered}$$
Putting these values in the above formula, we get:
Momentum = 10 × 10 kg.m/s = 100 kg.m/s

Answer:

The quantity of motion of a body which is equal to the product of the mass and velocity of the body is known as momentum of body. It is a vector quantity and is expressed in kg.m/s.

The momentum of a body is defined as the product of its mass and velocity.
Thus, momentum = mass × velocity
p = m × v

The momentum of a body depends on two factors i.e., mass and velocity of the body.

For example,
Given that:
mass, m = 5 kg
velocity, v₁ = 20 m/s
Therefore, momentum of a body moving with velocity v₁, p₁ = m × v₁
= 5 × 20 = 100 kg.m/s

Now,
mass, m = 5 kg
velocity, v₂ = 0.20 m/s
Therefore, momentum of a body moving with velocity v₁, p₂ = m × v₁
= 5 × 0.20 = 1 kg.m/s
Change in the momentum of a body = p₁ − p₂
                                                          = 100 − 1
                                                          = 99 kg.m/s

Answer:

(a) Force is defined as the push or pull on an object. Force causes an object to move, to speed up, slow down, change shape or change direction.

(b) Force can produce the following effects:

1. It can move a stationary body.
2. It can stop a moving body.
3. It can change the speed of a moving body.
4. It can change the direction of a moving body.
5. It can change the shape (and size) of a body.

Answer:

(a) The force of an engine can move a stationary car.

(b) The force of brakes can stop a moving car.

(c) Suppose one is riding a bicycle at a certain speed. Now, if someone pushes the moving bicycle from behind, then the speed of bicycle increases and it will move faster. On the other hand, if someone pulls the moving bicycle from behind then the speed of bicycle decreases and it will move slower. Thus, a push or pull can change the speed of the moving bicycle. As push or pull is a force, we can say that a force can change the speed of a moving bicycle (or any other moving body).

(d) If we blow air from our mouth towards the smoke rising up from a burning incense stick (agarbatti), then the direction of motion of the smoke changes. In this case, the force exerted by the blowing air changes the direction of the moving smoke.

(e) The shape of kneaded wet clay (geeli mitti) changes when a potter converts it into pots of different shapes and sizes. This happens because the potter applies force on the kneaded wet clay.

Answer:

(a) Balanced forces: If the resultant of all the forces acting on a body is zero, the forces are called balanced forces.
Example: When we push a concrete wall with our hands the wall doesn't move. This is because the force by us is balanced by the other forces acting on the wall.

Unbalanced force: If the resultant of all the forces acting on a body is not zero, the forces are called unbalanced force.
Example: If we push a toy car lying on the ground, we find that the toy car starts moving. This is because the force exerted by our hand is not balanced by the other forces acting on the toy car.

(b) The balanced forces change the shape of the rubber ball when we squeeze it.

When we press a rubber ball between our two hands, the shape of the  ball alters from spherical to oblong. This is because two equal and opposite forces (balanced force) are applied by our hands.

Answer:

(a) When a bus turns a corner sharply, the passengers tend to fall sideways because of their tendency to continue moving in the straight line (inertia).

(b) It is a common observation that road accidents due to vehicles travelling at high speeds are much worse than those with vehicles at low speeds. This is because the momentum of vehicles running at greater speeds is very high and causes a lot of damage to the vehicles and injures the passengers during the collision.

Answer:

(a) balanced force         
This is because a balanced force changes the shape of the object.

Answer:

(c) to resist a change in its state of motion
Inertia is the tendency of an object to resist a change in its state of motion.

Answer:

(c) unbalanced force      
Unbalanced forces are responsible for producing a change in the state of motion of a body. So when we talk of a force, it usually means unbalanced force.

Answer:

(a) accelerated
When the coin is tossed it was also moving with the horizontal speed of the train. The coin falls behind because the train is in an accelerated motion and no force is acting on the coin to speed up along with the train.

Answer:

(c) Newton’s first law of motion    
This is because beating the carpet with a stick  makes the carpet move to-and-fro quickly, but the dust particles tend to remain at rest due to their inertia and get separated from the carpet.

Answer:

(b) move forward
This is because of the inertia of the water in the tank that makes it remain in its state of motion even though the water tanker has stopped moving.

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(b) unbalanced force    
This is because an  unbalanced force is responsible to bring about a change in the state of motion of an object.

Answer:

(c) mass of the object
The inertia of a moving object depends on the mass of the object. Heavier objects tend to resist a change in their state more than the lighter objects do.

Answer:

(a) balanced forces act on the balloon.   
Balanced forces are responsible for bringing about a change in the shape of an object.

Answer:

(b) change in shape of the body      
Unbalanced forces tend to change the state of motion of a body.

Answer:

The wall will receive equal momentum from both the balls. This is because both the balls have equal mass and equal velocity.

Answer:

If we stop pedalling a bicycle, moving at a uniform speed, it does not go on moving forever. It eventually comes to rest after some time. This is because the moving bicycle has been compelled to change its state of uniform motion by the external force of air resistance and friction. If there were no air resistance and no friction to oppose the motion of the bicycle, then, according to the first law of motion, the moving bicycle would go on moving forever on a horizontal road. It cannot stop by itself.

Answer:

(i) We know that:
Momentum = mass × velocity
                   = m × v
Here, mass, m = 500 g
We can convert grams (g) to kilograms (kg). A kilogram has 1000 grams.
m = 500 / 1000
m = 0.5 kg
Also, velocity, v =10 m/s
Putting these values in the above formula, we get:
Momentum = 0.5 × 10 = 5 kg.m/s

(ii) Its momentum at the highest point of its flight would be zero. At the maximum height the velocity of the ball is zero.

Answer:

These forces could be the frictional force and air resistance.
Force of friction contributes more towards the slowing down and stopping the car.

Answer:

(a) The general name of the forces such as X is unbalanced forces
(b) The general name of the forces such as Y is balanced forces.

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Force is the physical quantity which corresponds to the rate of change of momentum.

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$\mathrm{Force}=\frac{\mathrm{Change} \mathrm{in} \mathrm{Momentum}}{\mathrm{Time} \mathrm{Taken}}$

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Newton is the unit of force.

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One Newton is that force which when acts on a body of mass 1 kg produces an acceleration of 1 m/s² in it.

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The acceleration produced in a body is directly proportional to the force acting on it.

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If the mass of a body and the force acting on it are both doubled, the acceleration remains the same.

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Force is the physical quantity whose unit is ‘Newton’.

Answer:

Principle of conservation of momentum is involved in the working of a jet aeroplane.

Answer:

A rocket works on the principle of conservation of momentum.

Answer:

The given statement is true. A rocket propulsion system works on the principle of conservation of momentum.

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A force of 1 Newton produces an acceleration of 1 m/s2 in a body of 1 mass kg.

Answer:

We know that:
Force = mass × acceleration
          = m × a
Here, mass, m = 10 kg
force, F = 5 N
Putting these values in the above formula, we get:
5 N = 10 × acceleration
$$\begin{gathered} \Rightarrow \mathrm{acceleration}=\frac{5}{10} \\ \Rightarrow \mathrm{accleration}=0.5 \mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Answer:

According to Newton’s third law of motion, the floor exerts a force of 250 N on her in the upward direction.

Answer:

Mass (of the car) is the physical quantity which makes it easier to accelerate a small car than a large car.

Answer:

(a) To every action, there is an equal and opposite reaction.
(b) Momentum is a vector quantity. Its unit is kg.m/s.
(c) Newton’s second law of motion can be written as Force = mass × acceleration or Force = rate of change of momentum.
(d) Forces in a Newton’s third law pair have equal magnitude but act in opposite directions.
(e) In collisions and explosions, the total momentum remains constant, provided that no external force acts.

Answer:

The given equation gives us a relationship between 'force' and 'acceleration' according to the Newton's second law of motion.           
F = m × a
where,
m = mass of a body
a = acceleration of the body
F = force acting on the body

Answer:

While rowing the boat, the  boatman pushes the water backwards with the oar so that the water exerts an equal and opposite push on the boat which makes the boat move forward. In fact, harder the boatman pushes back the water with oars, greater is the force exerted by the water and faster the boat moves forward.

Answer:

When a bullet is fired from a gun, the force pushing the bullet forward is equal to the force pushing the gun backward. However, because of the high mass of the gun, it moves only a little distance backward and gives a backward jerk or kick to the shoulder of the gunman.

Answer:

In a horse cart, the horse pushes the ground in backward direction. According to Newton’s third law of the motion, the ground pushes the horse in forward direction. Thus, the horse moves in the forward direction. As the cart is attached to the horse, the cart too moves in the forward direction.

Answer:

The hot gases, produced by the rapid burning of the fuel, rush out of a jet at the bottom of the rocket at a very high speed. The equal and opposite reaction force of the downward going gases pushes the rocket upwards. A rocket can propel itself even in vacuum because it does not require air for obtaining uplift or for burning its fuel.

Answer:

Action and reaction act on different bodies. The action and reaction forces are equal in magnitude but they do not always produce equal acceleration in the two bodies on which they act.

Answer:

When a man jumps out of a boat to the bank of the river, the boat moves backwards, away from him. This is due to the fact that to step out of the boat, the man pushes the boat with his foot in backward direction. The push of the man on the boat is the action. The boat exerts an equal force on the man in forward direction which enables him to move forward. This force exerted by the boat on the man is reaction. Since the boat is floating on water and not fixed, it moves backward due to the force exerted by the man.

Answer:

On the slippery ground, the friction is much less and we cannot exert a backward action force on it which would produce a forward reaction force on us. Hence, it becomes difficult to walk on a slippery road.

Answer:

A runner presses the ground with his feet before he starts his run to receive a large reaction force by the ground on which he exerts an action force, in the forward direction. In this way, he can gain a great speed.

Answer:

Here, mass of bullet = 60 g
                                 $=\frac{60}{1000}$
                                  = 0.06 kg
velocity of bullet = 500 m/s
mass of gun = 5 kg
Now, putting these values in the formula:
Mass of bullet × Velocity of bullet = Mass of gun × Recoil velocity of gun
We get,
0.06 × 500 – 5 × Recoil velocity of gun
Recoil velocity of gun$=\frac{0.06\times 500}{5}$
                                   $$\begin{gathered} =\frac{0.06\times 500}{5} \\ =\frac{0.06\times {\cancel{500}}^{100}}{5} \\ =0.06\times 100 \end{gathered}$$
Recoil velocity of gun = 6 m/s

Answer:

Here,
Mass of the bullet, m = 10 g = 0.01 kg
Velocity of the bullet, v = 200 m/s
Mass of the target, M = 2 kg
Mass of the (target+bullet) after hitting = V (say)

Momentum of the system before hitting = (0.01)(200) + (2)(0) = 2
Momentum of the system after hitting = (2 + 0.01)V
(after hitting the bullet sticks to the target)

Now,
By law of conservation of momentum,

Momentum of the system before hitting = Momentum of the system after hitting
⇒ 2 = (2 + 0.01)V
⇒ V = 0.995 m/s

This is the velocity with which the bullet and the target moves after hitting.

Answer:

The body gains speed 30 m/s in 1 s. So, the acceleration is,
a = 30/1 = 30 m/s²
Mass, m = 2 kg
Force = mass × acceleration
Force = m × a
          = 2 × 30 = 60
The magnitude of force = 60 N

Answer:

Here, mass, m = 5kg
Let us calculate the value of acceleration by using the first equation of motion,
Given that:
initial velocity, u = 10 m/s
final velocity, v = 35 m/s
time taken, t = 25 seconds
Putting these values in the equation, we get:
v = u + at
⇒ 35 = 10 + a × 25
⇒ 35 = 10 + 25a
⇒ 35 − 10 = 25a
⇒ 25 = 25a
$$\begin{gathered} \Rightarrow a=\frac{25}{25} \\ \Rightarrow a=1 m/s^2 \end{gathered}$$
Now, putting m = 5 kg and a = 1 m/s² in equation we get,
Force = mass × acceleration
Force = m × a
Force = 5 × 1
Force = 5 N

Answer:

Let us first calculate the retardation $=\frac{\left(v-u\right)}{t}$
                                                           $$\begin{gathered} =\frac{\left(0-20\right)}{10} \\ =\frac{-20}{10} \\ =\frac{-2\cancel{0}}{1\cancel{0}} \\ =-2 \mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Now, we are going to find retarding force = mass × acceleration
                                                                    = 2400 kg × −2
                                                                    = −4800 N
The negative sign implies that the force on the car is acting opposite to the motion of the car.

Answer:

We are going to find acceleration
Force = mass × acceleration                                                                     
$$\begin{gathered} 100=20\times a \\ \Rightarrow a=\frac{100}{20} \\ \Rightarrow a=5 \end{gathered}$$
Now, putting these values in the equation:
$$\begin{gathered} v=u+at \\ \Rightarrow 100=0+5\times t \\ \Rightarrow 100=5t \\ \Rightarrow t=20 \end{gathered}$$
So, the required time is 20 s.

Answer:

We are going to find acceleration
Force = mass × acceleration
10 = 2.5 × a
$$\begin{gathered} \Rightarrow \frac{10}{2.5}=a \\ \Rightarrow \frac{10\times 10}{2.5 \times 10}=a \\ \Rightarrow a=4 \end{gathered}$$
Now, putting these values in the equation:
$$\begin{gathered} v=u+at \\ \Rightarrow 20=0+4\times t \\ \Rightarrow 20=4t \\ \Rightarrow \frac{20}{4}=t \\ \Rightarrow t=5s \end{gathered}$$

Answer:

(a) Momentum = Mass × velocity
= 10 × 4
= 40 kg.m/s

(b) Momentum = Mass × velocity
= 10 × 8
= 80 kg.m/s

(c) The gain in momentum per second = Momentum Gaintime
$$\begin{gathered} =\frac{80-40}{2} \\ =\frac{40}{2} \\ =20 \mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

(d) Force is the rate of change of momentum or the momentum gain or lost per second.
So, force = 20 kg.ms/² = 20 N

Answer:

Mass of bullet, m = 30 g
$$\begin{gathered} =\frac{30}{1000}\mathrm{kg} \\ =0.03 \mathrm{kg} \end{gathered}$$
Velocity of bullet, v = 100 m/s
Mass of gun, M = 3 kg
$$\begin{gathered} \mathrm{Recoil} \mathrm{velocity} \mathrm{of} \mathrm{gun}, \mathrm{V}=-\frac{0.03\times 100}{3} \\ \Rightarrow \mathrm{V}=-\frac{3}{3} \\ \Rightarrow \mathrm{V}=-1 \mathrm{m}/\mathrm{s} \end{gathered}$$

Answer:

Answer:

(a) Law of conservation of momentum is involved.
(b) Newton’s second law of motion is involved.
(c) Newton’s third law of motion is involved.
(d) Newton’s first law of motion is involved.

Answer:

(a) Newton’s Second law of motion states that the force ‘F’ acting on a body of mass ‘m’ producing acceleration ‘a’ is equal to the product of the mass and acceleration of the body. That is, F = ma
It can be derived from the concept of momentum.
Suppose a body of mass ‘m’ has initial velocity ‘u’ and after time ‘t’ its velocity becomes ‘v’. The initial momentum is, P_i = mu
The final momentum is P_f = mv
The change in momentum with respect to time ‘t’ is
= (mv − mu)/t = m (v − u)/t = F …….(1)
We know, acceleration, a = (v − u)/t
So, (1) implies,
F = m(v − u)/t = ma
Which is Newton’s Second law of motion.

(b) (i) Final velocity, v = 0 (because the car is brought to rest)
Distance covered, s = 50 m
So, Force = mass × acceleration
But we do not know the value of a.
Making use of the third equation of motion we get,
v² − u² = 2as
⇒ 0 − 20² = 2 × a × 50
⇒ −400 = 100a
⇒ a = −4
The acceleration = −4 m/s²

(ii) Force = mass × acceleration
Mass = 1000 kg
Force  = 1000 × (−4)
           = − 4000 N
Unbalanced force acting on the vehicle is −4000 N.

Answer:

(a) By moving the hand backwards, a fielder increases the time of action of the force on his hands. When the time increases, the force reduces and the chances of the fielder getting hurt and dropping the ball decreases.

(b) Mass of the ball, m = 150 g = 0.15 kg
Initial velocity of the ball, u = 30 m/s
Initial momentum of the ball, p_i = mu = 4.5 kg.m/s
The player’s hand stops the ball in 0.05 s.
Thus, final momentum of the ball is, p_f = 0
So, change in momentum of the ball = p_f − p_i
= 0 − 4.5
= −4.5 kg.m/s
So, rate of change of momentum is = −4.5/0.05 = −90 N
This is the force exerted by the hand on the ball.
So, the force exerted by the ball on the hand is = 90 N

Answer:

(a) According to Newton’s third law of motion, whenever one body exerts a force on another body, the second body exerts an equal and opposite force on the first body.

Examples:
(i) Jet airplanes utilize the principle of action and reaction. In the modern jet aircraft, the hot gases obtained by the rapid burning of fuel rush out of a jet from the rear end of the aircraft at a great speed. The equal and opposite reaction of the backward-heading gases pushes the aircraft forward at a great speed.

(ii) While rowing a boat, the boatman pushes the water backwards with the oars. The water exerts an equal and opposite push on the boat which makes the boat move forward. In fact, harder the boatman pushes back the water with the oars, greater is the reaction force exerted by water and faster moves the boat, in forward direction.

(b) When a fireman directs a powerful stream of water on fire from a hose pipe, he has to hold the hose pipe strongly because of its tendency to go backwards. The backward movement of the hose pipe is due to the backward reaction of the water rushing through it in the forward direction at a great speed.

Answer:

(a) The law of conservation of momentum states the total momentum of a system remains unchanged in the absence of any external force.

(b) (i) A rocket taking off from ground
Answer: In rocket, a large volume of gases produced by the combustion of fuel is allowed to escape through it in the backward direction. Due to the very high velocity, the backward rushing gases have a large momentum. They impart an equal and opposite momentum to the rocket due to which the rocket moves forward with a great speed.

(ii) Jet aeroplanes utilize the principle of action and reaction. In modern jet aircrafts, the hot gases obtained by the rapid burning of fuel rush out of a jet at the rear end of the aircraft at a great speed. The equal and opposite momentum of the  gases heading backwards pushes the aircraft forward at a great speed.

Answer:

(a) If the inflated balloon is released with its mouth untied in the downward direction, then it will move upwards because the air rushes out of balloon in the downward direction. The equal and opposite reaction of downward thrust of air pushes the balloon upwards.

(b) Force of unloaded truck:
m = 2000 kg
a = 0.5 m/s²
Force = mass × acceleration
          = 0.5 × 2000
          = 1000 N
Force of loaded truck:
We have to find maximum acceleration,
M =  [2000+2000]
Force = mass × acceleration
⇒ 1000 = a × 4000
$$\begin{gathered} \Rightarrow \frac{1000}{4000}=a \\ \Rightarrow a=0.25 \end{gathered}$$
The maximum acceleration when it is carrying a load of 2000 kg is 0.25 m/s².

Answer:

(c) momentum

The chemicals inside the rocket burn and produce a high-velocity blast of hot gases which move out through the tail nozzle of the rocket. As these gases move in downward direction with tremendous speed, the rocket moves up to balance the momentum of gases.

Answer:

(b) 0 N  
The object will keep on moving on a frictionless horizontal surface by itself due to Newton’s First law of motion.

Answer:

(b) kg
The quantity is mass and it is expressed in kilograms.

Answer:

(b) always act on different bodies in opposite directions.

Answer:

(b) kg.ms^-1

Answer:

(d) 500 N
This is because the ground exerts an equal and opposite force on the boy.

Answer:

(c) Tata Nano
Because the mass of Tata Nano is the least among the four and acceleration is inversely proportional to the mass of the object.

Answer:

(c) 0.25
Acceleration = Force / Mass
                     = 5 / 20
                     = 0.25

Answer:

(b) A force can accelerate a lighter vehicle more easily than a heavier vehicle which are moving.
Since, F = ma
⇒ a = F/m
Lesser the mass, higher the acceleration.

Answer:

(b) reduce the force exerted by the ball
He does this to increase the change in momentum time of the ball. This helps him to save himself from getting hurt by the ball.

Answer:

Car seat-belts are designed to be stretchable, as stretching the seat-belt allows the large momentum of a passenger to reduce gently and the passenger is prevented from being thrown forward violently. Therefore, major injuries can be prevented if the car suffers a collision.

Answer:

When a parachutist lands on the ground, the momentum he has is high enough to hurt him on hitting the ground. Rolling on the ground just after landing will convert the kinetic energy of fall into rotational energy which will be dissipated gradually by the friction of the ground. Thus, the parachutist will have a safe landing if he rolls on landing.

Answer:

Air is necessary for an aircraft to be able to fly. Aircraft cannot fly on moon in the absence of air as the pressure difference between the upper and lower part of the wing is required for producing lift. Moreover, air is also necessary to burn the fuel of the plane.

Answer:

Small animals have low mass and hence their momentum is small. So, when they fall from a considerable height, their momentum is not large enough to cause considerable damage to their bodies. However, falling from too great a height will definitely kill them.

Answer:

Momentum = Momentum of the boy + Momentum of the trolley
= Mass of boy × velocity of boy +Mass of trolley × Velocity of trolley
Momentum = Mass of the boy and trolley × common velocity
⇒ 280  = (50+20) × common velocity
⇒ 280 = 70 × common velocity
⇒ $\frac{280}{70}=$common velocity
⇒ 4 = common velocity

Hence, common velocity is 4 m/s.

Answer:

The force F₁ exerted by girl is the ‘action’ and the force F₂ exerted by the boat is the ‘reaction’.
Now, momentum of the girl in one direction must be equal to the momentum of the boat in opposite direction.
m₁ × v₁ = m₂ × v₂
⇒ 50 × 3 = 300 × v₂
⇒ v₂ = 0.5
Hence, velocity with which the boat begins to move backwards is 0.5 m/s.

Answer:

Common velocity just after the collision if they move off together will be:
$v=\frac{\left(m_1\times u_1\right)+\left(m_2+u_2\right)}{m_1+m_2}$
m₁ = 500kg,
u₁ = 4 m/s
m₂ = 1500kg
u₂ = 2 m/s
$$\begin{gathered} v=\frac{\left(500+4\right)+\left(1500\times 2\right)}{500+1500} \\ \Rightarrow v=\frac{2000+3000}{2000} \\ \Rightarrow v=\frac{5000}{2000} \\ \Rightarrow v=\frac{5\cancel{000}}{2\cancel{000}} \\ \Rightarrow v=2.5 \mathrm{m}/\mathrm{s} \end{gathered}$$
This is their common velocity after collision.

Answer:

According to the law of conservation of momentum, the two momenta given are equal to each other.
Before collision, momentum of the first ball is = (1)(2) = 2 kg.m/s
Before collision, momentum of the second ball = (1)(0) = 0

After collision, momentum of the first ball = (1)(0) = 0
After collision, momentum of the second ball is = (1)(v)

Now,
2 + 0 = 0 + 1v
⇒ v = 2
The velocity of Y after the collision is 2m/s.

Answer:

m₁ × v₁ = m₂ × v₂
m₁ = 2000 kg,
v₁ = 10 m/s
m₂ = 500 kg
v₂ = ?

2000 × 10 = 500 × v₂
20000 = 500 × v₂
v₂ = 20000/500
    = 40 m/s
The velocity of car B is 40 m/s.

Answer:

Here, mass of bullet = 20 g
                                 $$\begin{gathered} =\frac{20}{1000}\mathrm{kg} \\ =0.02 \mathrm{kg} \end{gathered}$$
Velocity of bullet = 400 m/s
Momentum of the bullet before hitting the man is = (0.02)(400) = 8 kg.m/s
After hitting the man the bullet stops and falls on the ground.
Mass of mass, M = 80 kg
If v is the velocity of the man after being hit by the bullet then,
Mv = 8
⇒ v = 8/80 = 0.1 m/s
This is the required velocity of the man.