Solution-Class 9-Science-Chapter-1-Law of Motion-Maharashtra Board

(1)

(2)

(3)

The minimum distance between the start and finish points of the motion of an object is called the displacement of the object.
(Answer of question is self explanatory therefore there is no question of explanation)

Deceleration is negative acceleration.
When a body is decelerating, it means its speed is decreasing speed. An acceleration with a negative also shows that the speed of the body is decreasing.

When an object is in uniform circular motion, its velocity changes at every point.

• In uniform circular motion, speed is uniform, velocity is not uniform.
• The magnitude of velocity remains constant, but the direction of velocity changes continuously with time.

During collision total momentum remains constant.
Momentum of the system before collision = Momentum of the system after collision

The working of a rocket depends on Newton’s third law of motion.

• The burning fuel inside the rocket creates a forward push on the rocket. This forward push creates an equal and opposite push on the exhaust gases. Thus, the working of a rocket depends on Newton’s third law of motion- Every action force has an equal and opposite reaction force which acts simultaneously.

When an object falls freely to the ground, it is under the effect of a constant force known as force of gravity. No other forces act on it. This force of gravity is uniform near earth’s surface.  Hence by Newton's second law of motion, we can say that this constant force of gravity accelerates the freely falling object uniformly.

When two bodies interact, the action and reaction forces come into action. Even though their magnitude are same and their direction are opposite, their effects do not get cancelled because these action and reaction forces act on different bodies.

Momentum of a body is the product of its mass and velocity and the rate of change of momentum of a body is equal to the force applied i.e.
F=m(v−u)t

In the given information, both the balls move with same velocity,

We know force is directly proportional to mass (F∝m) therefore force required to stop the ball will be directly proportional to the mass of the ball.
As the mass of cricket ball is greater than the tennis ball, its momentum will be more than the tennis ball. Thus, greater force will be required to stop the cricket ball as compared to that of tennis ball.

Also cricket ball is harder than tennis ball therefore it is hard to stop the cricket ball than tennis ball.

Velocity of an object is said to be uniform when its speed and direction does not change. The velocity of an object at rest is zero all the time and does not even change the direction. Hence, the velocity of an object at rest is considered to be uniform.

• If we try to push an empty cart and a cart full of bricks, it would be easier to push an empty cart than the cart full of bricks. This happens because the inertia of the cart full of bricks is more than the empty cart and by Newton's first law of motion we know that more the inertia, more force is required to change the state of rest of a body.
• When a bat strikes a ball, the ball also exerts an equal (in magnitude) and opposite (in direction) force of reaction on the bat at the same time. The force on the ball increases its velocity and the force on the bat slows down its forward motion.
• When we place a book on table, the book does not fall. This is because the same amount of force is applied by the table on the book as is applied by the book on the table.
• Our walking is an example of Newton's third law of motion. When we walk we push the ground in backward direction with some force. The ground in reaction pushes us forward with the same force.
• A person, while swimming, pushes the water in the backward direction. At the same time he experiences an equal (in magnitude) and opposite (in direction) push in the forward direction, due to the force of reaction of water.

s₁=18m, s₂= 22m, s₃=22m t₁=3s, t₂=3s t₃=3s, Average speed=?

Average speed=\(\frac{\text{Total distance}}{\text{Total time}}\)

= \(\frac{s_1+s_2+s_3}{t_1+t_2+t_3}\)

= \(\frac{18m+22m+14m}{3s+3s+3s}\)

= \(\frac{54m}{9s}\) = 6 m/s

∴ Average speed= 6 m/s

(i) m₁ = 16 kg, a₁ =  3 m/s² 
F = m₁ × a₁
F = 16 × 3 = 48 N
(ii) Now, F = 48 N, m₂ =24 kg
F = m₂ × a₂
48 = 24 × a₂
a₂ = 2 m/s²

Given,

Mass of bullet, m₁ = 10 g

Initial speed of bullet, u₁ = 1.5 m/s

Mass of plank, m₂ = 90 g

Initial speed of plank, u₂ = 0

From law of conservation of momentum,

 m₁u_{1 +} m₂u₂ = m₁v₁ + m₂v₂

Since, the bullet gets embedded in the plank and both move with the same speed, so v₁ = v₂ = v
So, we can rewrite the equation as 

 m₁u_{1 +} m₂u₂ = (m₁ + m₂)v

10 ×1.5 + 90 × 0 = (10 + 90)v

15 = 100v ⇒v = 0.15 m/s

∴ velocity = 0.15 m/s

Given: s₁=100m, s₂= 80m, s₃=45m t₁=40s, t₂=40s t₃=20s, Average speed=?

Average speed = \(\frac{\text{Average distance}}{\text{Average time}}\)

= \(\frac{s_1+s_2+s_3}{t_1+t_2+t_3}\)

= \(\frac{100m+80m+45m}{ 40s+40s+20s}\) 

=\(\frac{225m}{100s}\)

Average speed  = 2.25 m/s