Force & Laws Of Motion - Practice Test, Class 9 Science - Class 9 MCQ

• Initial velocity of the car = 45 km/hr


• Final velocity of the car = 63 km/hr


• Time interval = 10 sec

• Initial velocity = 45 km/hr = 12.5 m/s


• Final velocity = 63 km/hr = 17.5 m/s


• Acceleration (a) = (Final velocity - Initial velocity) / Time interval = (17.5 - 12.5) / 10 = 0.5 m/s²

• Using the equation: Final velocity² = Initial velocity² + 2 * acceleration * distance


• Distance = (Final velocity² - Initial velocity²) / (2 * acceleration) = (17.5² - 12.5²) / (2 * 0.5) = 150 m

• The distance traveled by the car during the interval of 10 sec is 150 m.

• Definition: The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it.


• Application in Rockets: Rockets work by expelling mass at high speeds in one direction, which generates a reaction force propelling the rocket in the opposite direction.


• Newton's Third Law: According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the rocket expels mass, it gains momentum in the opposite direction.


• Conservation of Momentum: The total momentum of the rocket and the expelled mass remains constant before and after the expulsion. This conservation of momentum ensures that the rocket can move forward in space.


• Mathematical Representation: The mathematical representation of conservation of momentum in rockets is given by the equation:
  \[ m_{rocket} \cdot v_{rocket} = m_{exhaust} \cdot v_{exhaust} \]
  where \(m\) represents mass and \(v\) represents velocity.

• Mass of object = 2 kg


• Velocity of object = 4 m/s


• Frictionless horizontal table

• Since the object is moving with a constant velocity on a frictionless surface, the net force acting on it is zero (according to Newton's first law).


• The force required to keep an object moving with a constant velocity is equal to the force of friction acting in the opposite direction.


• However, since there is no friction in this case, the force required to keep the object moving with the same velocity is also zero.

Therefore, the correct answer is 0 N.

• Uniform force: When a body is acted upon by a uniform force, it will cause a change in the speed or direction of motion of the body.


• Zero force: If there is zero force acting on a body, there will be no change in the speed or direction of motion of the body.


• An unbalanced force: An unbalanced force will cause a change in the speed or direction of motion of a body. This occurs when the net force acting on the body is not zero, resulting in acceleration or deceleration.


• Balanced force: A balanced force occurs when the forces acting on an object are equal in magnitude and opposite in direction. In this case, there will be no change in the speed or direction of motion of the body.

Therefore, the correct answer is that there will be a change in the speed or in the direction of motion of a body when it is acted upon by an unbalanced force.

• Definition of Inertia: Inertia is the resistance of any physical object to any change in its state of motion, including changes to its speed and direction.


• Measure of Mass: Inertia is directly related to the mass of an object. The greater the mass of an object, the greater its inertia. This means that objects with more mass require more force to change their state of motion.


• Newton's First Law: Newton's first law of motion states that an object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an external force. This is a direct result of the concept of inertia.


• Relationship with Force: Inertia and force are related concepts. Force is required to overcome an object's inertia and cause it to accelerate or decelerate. The relationship between force and acceleration is described by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.


• Units of Inertia: The SI unit of inertia is the kilogram (kg), which is also the unit of mass. This further emphasizes the direct relationship between inertia and mass.

• F = ma: The formula to find force is F = ma, where F represents force, m represents mass, and a represents acceleration. This formula is derived from Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

• First, we need to determine the mass of the object in question. This can be done by measuring the mass directly or using known values.


• Next, we need to calculate the acceleration of the object. This can be done by measuring the change in velocity over time or using other known values.


• Once we have the mass and acceleration values, we can plug them into the formula F = ma to find the force acting on the object.


• It is important to ensure that the units of mass and acceleration are compatible (e.g., kg for mass and m/s^2 for acceleration) to get the correct unit for force (e.g., Newton).

• Constant speed and acceleration: When a body moves with constant speed but still accelerates, it means that the direction of its velocity is changing, even though the magnitude of the velocity remains constant.


• Circular path: In a circular path, the direction of motion of the body is constantly changing. This change in direction indicates that the body is accelerating, even if the speed remains constant.


• Centripetal acceleration: In the case of a body moving in a circular path with constant speed, there is a centripetal acceleration acting towards the center of the circle. This acceleration is responsible for changing the direction of the body's velocity.


• Acceleration without change in speed: The centripetal acceleration does not affect the speed of the body but causes it to accelerate due to the change in direction.

• Mass of the hammer (m) = 500 g = 0.5 kg


• Initial velocity of the hammer (u) = 50 m/s


• Time taken to stop (t) = 0.01 s

• Final velocity of the hammer (v) = 0 m/s (since the hammer stops)


• Using the equation of motion: \( v = u + at \), where a is the acceleration


• Acceleration (a) = \( \frac{(v - u)}{t} = \frac{(0 - 50)}{0.01} = -5000 m/s^2 \) (the negative sign indicates deceleration)

• Force (F) = Mass (m) x Acceleration (a)


• Substitute the values: \( F = 0.5 kg \times -5000 m/s^2 = -2500 N \)

• The force of the nail on the hammer is 2500 N.

• Acceleration: Acceleration is the rate at which an object changes its velocity. It is a vector quantity, which means it has both magnitude and direction.


• Net Force: Acceleration is directly proportional to the net force acting on an object. The direction of acceleration is in the direction of the net force.


• Newton's Second Law: According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that if the net force acting on an object is in a certain direction, the acceleration will also be in that direction.


• Initial Velocity and Displacement: While initial velocity and displacement play a role in the motion of an object, the direction of acceleration is determined by the net force acting on the object, not by its initial velocity or displacement.

Therefore, the correct answer is C: Of the net force. Acceleration always acts in the direction of the net force acting on an object.

• A body of weight W is suspended from the ceiling through a rope of weight R.


• The total force acting on the rope is the sum of the weight of the body and the weight of the rope.

• The force exerted by the ceiling on the rope is equal to the total weight hanging from the rope, which is the sum of the weight of the body and the weight of the rope.


• Therefore, the force exerted by the ceiling on the rope is W + R.


• So, the correct answer is C: W + R.

• Newtons laws: Newton's laws of motion are fundamental principles in classical physics that describe the relationship between the motion of an object and the forces acting on it.


• Particles at rest: Newton's laws are applicable to particles at rest as they are in a state of equilibrium and there is no motion involved.


• Particles moving slowly: Newton's laws are also valid for particles moving slowly as the forces acting on them can be accurately described by these laws.


• Particles moving with high velocity: When particles move with high velocity, they approach the speed of light and the laws of classical physics, including Newton's laws, start to break down.


• Particles moving with velocity comparable to the velocity of light: At velocities approaching the speed of light, particles exhibit relativistic effects that cannot be described by Newton's laws. In this case, we need to use Einstein's theory of relativity to accurately describe the motion of particles.

Therefore, Newton's laws do not hold good for particles moving with velocities comparable to the velocity of light and we need to rely on the principles of relativistic physics to understand their behavior accurately.

• Force acts on the body: The momentum of an object depends on the force acting on it. The greater the force applied, the greater the change in momentum.


• Mass of the body: The momentum of an object is directly proportional to its mass. A heavier object will have more momentum compared to a lighter object if they are moving at the same velocity.


• Velocity of the body: The momentum of an object also depends on its velocity. An object moving at a higher velocity will have greater momentum compared to the same object moving at a lower velocity.


• Both mass and velocity of the body: Ultimately, momentum is a combination of both mass and velocity. The momentum of an object can be calculated by multiplying its mass by its velocity.

• Rest: The 1st law of motion states that an object at rest will remain at rest unless acted upon by an external force. This means that if there is no force acting on an object, it will continue to stay at rest.


• Velocity: While velocity is related to motion, the 1st law of motion specifically deals with objects at rest or in a state of constant velocity.


• Motion: The 1st law of motion does not define motion itself, but rather the conditions under which an object will remain in its current state of motion or rest.


• Force: The correct definition given by the 1st law of motion is that an object will remain in its state of motion unless acted upon by an external force. This means that a force is required to change the motion of an object, whether that means starting it moving or stopping it from moving.

Therefore, the 1st law of motion defines force as the factor that influences the motion of an object, whether that motion is at rest or in a state of constant velocity.

• Existence of pair of forces in nature: According to the 3rd law of motion, for every action, there is an equal and opposite reaction. This means that whenever one object exerts a force on another object, the second object exerts a force of equal magnitude but in the opposite direction. These two forces form a pair of forces that act on the two interacting objects.


• Conservation of momentum: The existence of pair of forces in nature ensures the conservation of momentum. When two objects interact with each other, the total momentum of the objects before and after the interaction remains constant. This principle is crucial in understanding the behavior of objects in motion.


• Examples of pair of forces: Common examples of pair of forces include a person pushing against a wall (the person exerts a force on the wall and the wall exerts an equal but opposite force on the person), a rocket launching into space (the rocket exerts a force downward and the exhaust gases exert an equal but opposite force upward), and a book resting on a table (the book exerts a force downward and the table exerts an equal but opposite force upward).


• Implications in everyday life: Understanding the 3rd law of motion and the existence of pair of forces in nature helps us explain various phenomena in our everyday lives, such as the motion of vehicles, the behavior of objects in collisions, and the operation of machines.