Laws of Motion MCQ Quiz - Objective Question with Answer for Laws of Motion - Download Free PDF

The correct answer is 15 ms^-1.

Key Points

• The position of the object is given by the equation x = a + bt², where a = 8.5 m, b = 2.5 m/s^-2, and t is time in seconds.
• To find the average velocity, the formula used is: v_avg = (x_final - x_initial) / (t_final - t_initial).
• At t = 2.0 s, the position x_initial = 8.5 + 2.5(2.0)² = 18.5 m.
• At t = 4.0 s, the position x_final = 8.5 + 2.5(4.0)² = 48.5 m.
• The average velocity is calculated as v_avg = (48.5 - 18.5) / (4.0 - 2.0) = 30 / 2 = 15 ms^-1.

Additional Information

• Average Velocity: It is defined as the total displacement divided by the total time taken. It gives the overall rate of change of position over a time interval.
• Position Equation: The equation x = a + bt² represents a quadratic relation where acceleration is constant, and the motion is uniformly accelerated.
• Constant Acceleration: In the equation, the coefficient b (2.5 m/s²) represents half of the acceleration. The full acceleration can be derived as 2b = 5.0 m/s².
• Instantaneous Velocity: The instantaneous velocity at any time t can be found by differentiating x with respect to t: v = dx/dt = 2bt.
• Units of Measurement: Displacement is measured in meters (m), time in seconds (s), and velocity in meters per second (m/s).

The correct answer is Option 1.

Key Points

• Inertia is the property of matter that describes an object's tendency to resist changes in its state of motion or rest.
• Option 1 is incorrect because inertia alone does not cause an object to stop; it maintains the object’s current state of motion unless acted upon by external forces like friction or air resistance.
• An object moving in a straight line at constant velocity will continue indefinitely unless external forces act on it, according to Newton's first law of motion.
• Newton’s first law, also known as the law of inertia, states that an object at rest stays at rest and an object in motion stays in motion unless acted upon by an external force.
• External forces such as friction or gravity are responsible for bringing a moving object to rest, not inertia itself.

Additional Information

• Newton's First Law of Motion: Often called the law of inertia, it explains that an object will not change its motion unless a net external force is applied.
• Friction: A force that opposes motion, typically responsible for stopping moving objects when no additional force is applied.
• Gravity: A universal force of attraction that can influence the motion of objects, such as causing them to decelerate or come to rest.
• Inertia and Mass: The amount of inertia an object has is directly related to its mass; larger masses have greater inertia.
• Practical Examples: A ball rolling on a flat surface eventually stops due to friction, not inertia, while a spacecraft in the vacuum of space continues moving indefinitely due to the absence of external forces.

The correct answer is Mass.

Key Points

• Inertia is the property of an object that resists changes in its state of motion.
• It is directly related to the mass of an object; the greater the mass, the greater the inertia.
• An object with larger mass requires more force to change its state of motion compared to an object with smaller mass.
• Newton's First Law of Motion states that an object will remain at rest or in uniform motion unless acted upon by an external force, which is a description of inertia.
• For example, a heavy truck has more inertia than a small car, making it harder to start moving or stop once in motion.

 Additional Information

• Shape
  • The shape of an object does not affect its inertia. Inertia is solely dependent on mass.
  • For example, a cube and a sphere of the same mass will have the same inertia regardless of their different shapes.
• Acceleration
  • Acceleration is the rate of change of velocity of an object, not a property that affects inertia.
  • While acceleration can change the motion of an object, it doesn't determine the object's inertia.
• Velocity
  • Velocity is the speed of an object in a particular direction, and it does not influence the inertia of the object.
  • An object's inertia remains the same irrespective of its velocity.

The correct answer is Mass.

Key Points

• Inertia is the property of an object that resists changes in its state of motion or rest.
• The inertia of an object is directly proportional to its mass; the greater the mass, the greater the inertia.
• Mass is a measure of the quantity of matter in an object, and it determines how difficult it is to change the object's motion.
• Inertia is independent of other properties like shape, velocity, or acceleration.
• This fundamental concept is explained in Newton's First Law of Motion, which states that an object will remain at rest or in uniform motion unless acted upon by an external force.

Additional Information

• Newton's First Law of Motion: Also known as the Law of Inertia, it describes how an object will not change its motion unless acted upon by an external force.
• Types of Inertia:
  • Inertia of Rest: The tendency of an object to remain at rest.
  • Inertia of Motion: The tendency of an object to maintain its motion.
  • Inertia of Direction: The tendency of an object to maintain its direction of motion.
• Mass vs. Weight: Mass is an intrinsic property of an object, while weight is the force exerted by gravity on that mass (Weight = Mass × Gravitational Acceleration).
• Practical Examples of Inertia:
  • A passenger tends to move forward when a vehicle suddenly stops due to the inertia of motion.
  • A book lying on a table remains stationary unless pushed, due to the inertia of rest.
• Relation with Force: To overcome an object's inertia, a force proportional to its mass and desired acceleration must be applied (F = ma, as per Newton's Second Law).

The correct answer is Isaac Newton.

Key Points

• Isaac Newton formulated the Three Laws of Motion, which are fundamental principles describing the relationship between the motion of objects and the forces acting on them.
• These laws were first introduced in Newton's landmark work, "Philosophiæ Naturalis Principia Mathematica" (The Principia), published in 1687.
• The laws of motion laid the groundwork for classical mechanics, which is a branch of physics that deals with the motion of macroscopic objects.
• Newton's First Law, also known as the Law of Inertia, states that an object will remain at rest or in uniform motion unless acted upon by an external force.
• Newton's contributions to physics and mathematics earned him recognition as one of the most influential scientists in history.

Additional Information

• Newton's Second Law: This law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). It explains how the motion of an object changes when a force is applied.
• Newton's Third Law: It states that for every action, there is an equal and opposite reaction. This principle is fundamental in understanding interactions between objects.
• Inertia: A property of matter described in Newton's First Law, where an object resists changes in its state of motion unless influenced by an external force.
• Classical Mechanics: The branch of physics developed from Newton's laws, which deals with the motion of objects under forces and is used to analyze a wide range of physical phenomena.
• Philosophiæ Naturalis Principia Mathematica: Often referred to as "The Principia," this book not only introduced the laws of motion but also formulated the law of universal gravitation.

The correct answer is Mass.

Key Points

• Inertia is the property of an object that resists changes in its state of motion.
• It is directly related to the mass of an object; the greater the mass, the greater the inertia.
• An object with larger mass requires more force to change its state of motion compared to an object with smaller mass.
• Newton's First Law of Motion states that an object will remain at rest or in uniform motion unless acted upon by an external force, which is a description of inertia.
• For example, a heavy truck has more inertia than a small car, making it harder to start moving or stop once in motion.

 Additional Information

• Shape
  • The shape of an object does not affect its inertia. Inertia is solely dependent on mass.
  • For example, a cube and a sphere of the same mass will have the same inertia regardless of their different shapes.
• Acceleration
  • Acceleration is the rate of change of velocity of an object, not a property that affects inertia.
  • While acceleration can change the motion of an object, it doesn't determine the object's inertia.
• Velocity
  • Velocity is the speed of an object in a particular direction, and it does not influence the inertia of the object.
  • An object's inertia remains the same irrespective of its velocity.

The correct answer is Mass.

Key Points

• Inertia is the property of an object that resists changes in its state of motion or rest.
• The inertia of an object is directly proportional to its mass; the greater the mass, the greater the inertia.
• Mass is a measure of the quantity of matter in an object, and it determines how difficult it is to change the object's motion.
• Inertia is independent of other properties like shape, velocity, or acceleration.
• This fundamental concept is explained in Newton's First Law of Motion, which states that an object will remain at rest or in uniform motion unless acted upon by an external force.

Additional Information

• Newton's First Law of Motion: Also known as the Law of Inertia, it describes how an object will not change its motion unless acted upon by an external force.
• Types of Inertia:
  • Inertia of Rest: The tendency of an object to remain at rest.
  • Inertia of Motion: The tendency of an object to maintain its motion.
  • Inertia of Direction: The tendency of an object to maintain its direction of motion.
• Mass vs. Weight: Mass is an intrinsic property of an object, while weight is the force exerted by gravity on that mass (Weight = Mass × Gravitational Acceleration).
• Practical Examples of Inertia:
  • A passenger tends to move forward when a vehicle suddenly stops due to the inertia of motion.
  • A book lying on a table remains stationary unless pushed, due to the inertia of rest.
• Relation with Force: To overcome an object's inertia, a force proportional to its mass and desired acceleration must be applied (F = ma, as per Newton's Second Law).

The correct answer is The second law of motion is a scalar law.

Key Points

• Newton’s second law of motion is a vector law, not a scalar law, as it deals with quantities like force and acceleration, which have both magnitude and direction.
• The mathematical expression of the second law is F = ma, where 'F' and 'a' are vectors, and 'm' is a scalar quantity representing mass.
• This law is applicable to a single point particle, describing how a force acting on it results in acceleration in the direction of the force.
• The second law is a local relation, meaning the force 'F' at a specific point in space and time is directly related to the acceleration 'a' at that point and time.
• According to the second law, if the net external force (F) acting on a system is zero, the acceleration (a) of the system is also zero, implying the system is in equilibrium or moving at a constant velocity.

Additional Information

• Newton's Second Law of Motion:
  • It states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.
  • The equation is written as F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.
• Vector Quantities:
  • These are physical quantities that have both magnitude and direction, such as force, velocity, acceleration, and displacement.
  • Newton's second law inherently involves vector quantities, as force and acceleration must be aligned.
• Scalar Quantities:
  • These are quantities that only have magnitude and no direction, such as mass, speed, energy, and temperature.
  • Newton's second law is not scalar because it involves directional properties.
• Applications of Newton's Second Law:
  • It is widely used in engineering and physics to design vehicles, structures, and machinery by calculating forces and accelerations.
  • It also explains everyday phenomena like why heavier objects are harder to accelerate compared to lighter ones.

The correct answer is 15 ms^-1.

Key Points

• The position of the object is given by the equation x = a + bt², where a = 8.5 m, b = 2.5 m/s^-2, and t is time in seconds.
• To find the average velocity, the formula used is: v_avg = (x_final - x_initial) / (t_final - t_initial).
• At t = 2.0 s, the position x_initial = 8.5 + 2.5(2.0)² = 18.5 m.
• At t = 4.0 s, the position x_final = 8.5 + 2.5(4.0)² = 48.5 m.
• The average velocity is calculated as v_avg = (48.5 - 18.5) / (4.0 - 2.0) = 30 / 2 = 15 ms^-1.

Additional Information

• Average Velocity: It is defined as the total displacement divided by the total time taken. It gives the overall rate of change of position over a time interval.
• Position Equation: The equation x = a + bt² represents a quadratic relation where acceleration is constant, and the motion is uniformly accelerated.
• Constant Acceleration: In the equation, the coefficient b (2.5 m/s²) represents half of the acceleration. The full acceleration can be derived as 2b = 5.0 m/s².
• Instantaneous Velocity: The instantaneous velocity at any time t can be found by differentiating x with respect to t: v = dx/dt = 2bt.
• Units of Measurement: Displacement is measured in meters (m), time in seconds (s), and velocity in meters per second (m/s).

CONCEPT:

Retarding Force (F_retard)

F_retard = m x a

a = (v - u) / t

EXPLANATION:

• Given data:
  • Mass of the car (m) = 1000 kg
  • Initial velocity (u) = 72 km/h = 72 * (1000/3600) m/s = 20 m/s
  • Final velocity (v) = 0 m/s
  • Time taken to stop (t) = 0.2 s

• a = (v - u) / t
• = (0 - 20) / 0.2
• = -20 / 0.2
• = -100 m/s²

• F_retard = m * a
• = 1000 kg * (-100 m/s²)
• = -100,000 N
• The negative sign indicates that the force is in the opposite direction of the motion. The magnitude of the retarding force is:
  • 100,000 N or 100 kN

Therefore, the retarding force applied on the car to stop it is 100 kN.

The correct answer is Net external force on body.

Key Points

• In the second law of motion, F = ma, F represents the net external force acting on a body.
• The second law of motion states that the acceleration of a body is directly proportional to the net external force applied to it and inversely proportional to its mass.
• This law is expressed mathematically as F = ma, where 'F' is the net external force, 'm' is the mass of the body, and 'a' is the acceleration.
• Net external force is the vector sum of all the external forces acting on a body, excluding internal forces.
• The direction of the acceleration is the same as the direction of the net external force.

Additional Information

• Newton's Laws of Motion
  • Sir Isaac Newton formulated three laws of motion that describe the relationship between the motion of an object and the forces acting on it.
  • The first law, also known as the law of inertia, states that an object at rest stays at rest and an object in motion stays in motion unless acted upon by an external force.
  • The third law states that for every action, there is an equal and opposite reaction.
• Force
  • Force is a vector quantity that causes an object to move or change its velocity.
  • It is measured in newtons (N) in the International System of Units (SI).
• Mass
  • Mass is a measure of the amount of matter in an object.
  • It is a scalar quantity and is measured in kilograms (kg) in the SI unit.
• Acceleration
  • Acceleration is the rate of change of velocity of an object with respect to time.
  • It is a vector quantity and is measured in meters per second squared (m/s²) in the SI unit.

CONCEPT:

Kinematics and Vector Addition

• The displacement of an object is a vector quantity that has both magnitude and direction.
• When a vehicle accelerates from rest, the distance traveled can be calculated using the kinematic equation:

  s = ut + (1/2)at²

• For vector addition, the net displacement can be found by combining the displacements in each direction using the Pythagorean theorem.

EXPLANATION:

• First phase:

  Acceleration = 2 m/s² towards east

  Time = 10 s

  Initial velocity (u) = 0 (starting from rest)

  Distance traveled towards east (s_east) = ut + (1/2)at²

  • = 0 + (1/2) * 2 m/s² * (10 s)²
  • = (1/2) * 2 * 100
  • = 100 meters
• Second phase:

  Acceleration = 4√2 m/s² towards south

  Time = 10 s

  Distance traveled towards south (s_south) = ut + (1/2)at²

  • = 0 + (1/2) * 4√2 m/s² * (10 s)²
  • = (1/2) * 4√2 * 100
  • = 200√2 meters
• Net displacement:

  Use the Pythagorean theorem to find the resultant displacement (d):

  • d = √(s_east² + s_south²)
  • = √(100² + (200√2)²)
  • = √(10000 + 80000)
  • = √90000
  • = 300 meters

Therefore, the net displacement of the vehicle from the starting point is 300 meters.

The correct answer is Galileo.

Key Points

• Galileo Galilei, a renowned Italian physicist and astronomer, laid the foundation of the concept of inertia, which later became a cornerstone of Newton's First Law of Motion.
• He proposed that an object moving on a frictionless horizontal plane would continue to move at a constant velocity unless acted upon by an external force.
• This idea challenged the Aristotelian view that an external force is always required to maintain motion.
• Galileo's experiments with inclined planes helped him formulate the idea that resistance (e.g., friction) is what causes objects to slow down, not an inherent tendency to stop.
• His pioneering work on the laws of motion directly influenced Isaac Newton's formulation of classical mechanics.

Additional Information

• Inertia:
  • Inertia is the property of an object to resist changes to its state of motion or rest.
  • This concept was first systematically studied by Galileo and later refined by Newton.
• Newton's First Law of Motion:
  • Also known as the Law of Inertia, it states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
  • This law builds on Galileo's observations and experiments.
• Friction:
  • Friction is a force that opposes motion between two surfaces in contact.
  • Galileo identified friction as the primary reason why objects eventually come to rest in the real world.
• Galileo's Inclined Plane Experiment:
  • Galileo used inclined planes to slow down the motion of objects, allowing him to study their behavior more carefully.
  • These experiments demonstrated that objects accelerate uniformly when rolling down a slope, leading to his insights on motion.
• Transition from Aristotelian Physics:
  • Aristotle believed that continuous force was required for motion, a view disproved by Galileo's work.
  • Galileo's ideas marked the beginning of the shift to modern physics.

The correct answer is Second law of motion.

Key Points

• The Second Law of Motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration, expressed as F = ma.
• In the case of circular motion, the centripetal force (Fc) required to keep the body moving in a circle is given by Fc = mv²/R, where m is mass, v is velocity, and R is radius.
• The acceleration experienced in circular motion is centripetal acceleration, directed towards the center, and its magnitude is v²/R.
• This law forms the basis for understanding the relationship between force, mass, and acceleration in both linear and circular motion scenarios.
• Newton's Second Law is universally applicable and provides the mathematical foundation for analyzing motion and dynamics in physics.

Additional Information

• Circular Motion Terminology:
  • Centripetal Force: The inward force required to keep an object moving in a circular path.
  • Centripetal Acceleration: Acceleration directed towards the center of the circle, calculated as v²/R.
  • Uniform Circular Motion: Motion of an object traveling at a constant speed along a circular path.
• Newton's Laws of Motion:
  • First Law: A body remains at rest or in uniform motion unless acted upon by an external force.
  • Second Law: Force is directly proportional to the rate of change of momentum (F = ma).
  • Third Law: For every action, there is an equal and opposite reaction.
• Applications of Centripetal Force:
  • Satellite motion in orbit around Earth.
  • Vehicles negotiating curved paths on roads.
  • Amusement park rides such as roller coasters.
• Historical Context:
  • Newton formulated the Second Law of Motion as part of his groundbreaking work in "Philosophiæ Naturalis Principia Mathematica" (1687).
  • It revolutionized the understanding of motion and dynamics, forming the core of classical mechanics.

The correct answer is Isaac Newton.

Key Points

• Isaac Newton formulated the Three Laws of Motion, which are fundamental principles describing the relationship between the motion of objects and the forces acting on them.
• These laws were first introduced in Newton's landmark work, "Philosophiæ Naturalis Principia Mathematica" (The Principia), published in 1687.
• The laws of motion laid the groundwork for classical mechanics, which is a branch of physics that deals with the motion of macroscopic objects.
• Newton's First Law, also known as the Law of Inertia, states that an object will remain at rest or in uniform motion unless acted upon by an external force.
• Newton's contributions to physics and mathematics earned him recognition as one of the most influential scientists in history.

Additional Information

• Newton's Second Law: This law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). It explains how the motion of an object changes when a force is applied.
• Newton's Third Law: It states that for every action, there is an equal and opposite reaction. This principle is fundamental in understanding interactions between objects.
• Inertia: A property of matter described in Newton's First Law, where an object resists changes in its state of motion unless influenced by an external force.
• Classical Mechanics: The branch of physics developed from Newton's laws, which deals with the motion of objects under forces and is used to analyze a wide range of physical phenomena.
• Philosophiæ Naturalis Principia Mathematica: Often referred to as "The Principia," this book not only introduced the laws of motion but also formulated the law of universal gravitation.