50 Higher-Order Thinking Skills (HOTS) MCQs (Level 3) on Motion and Force, Physics (Unit-Wise MCQs Practice):
Whether you are preparing for board examinations, school tests, college assessments, university exams, entry tests, or competitive examinations, this comprehensive Motion and Force MCQs collection is designed to strengthen your conceptual understanding and problem-solving skills.
This chapter covers all the fundamental and advanced topics of motion and force, including scalar and vector quantities, displacement, distance, speed, velocity, acceleration, equations of uniformly accelerated motion, projectile motion, Newton's Laws of Motion, mass, weight, momentum, impulse, collisions, conservation of momentum, graph interpretation, and real-life applications of mechanics.
The MCQs are carefully organized into three progressive difficulty levels to help learners build confidence step by step:
- 100 Basic Conceptual MCQs – Develop a strong foundation by covering definitions, principles, formulas, and essential concepts.
- 100 Advanced & Numerical MCQs – Improve analytical and mathematical problem-solving skills through calculations and application-based questions.
- 50 Higher-Order Thinking Skills (HOTS) MCQs – Challenge your understanding with conceptual reasoning, graph analysis, multi-step problems, and competitive examination-style questions.
- 50 Challenging MCQs Quiz with Answers (1–50) – Carefully selected conceptual, numerical, and HOTS questions to strengthen problem-solving skills and prepare students for board and competitive examinations.
Every MCQ includes:
- ✔ Four carefully designed answer options
- ✔ Instant correct answer
- ✔ Detailed concept-based explanation
- ✔ Exam-focused learning approach
This collection is ideal for students preparing for Physics examinations at school, college, and university levels, as well as candidates appearing in engineering, medical, and other competitive entrance examinations. Teachers can also use these questions for classroom assessments, quizzes, assignments, and revision sessions.
By practicing these 250 carefully selected Motion and Force MCQs, you will improve your conceptual clarity, numerical problem-solving ability, graph interpretation skills, logical reasoning, and confidence in tackling objective-type Physics questions. Whether you are revising before an examination or strengthening your fundamentals, this comprehensive MCQ collection provides an excellent resource for complete chapter preparation and long-term success.
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Level-II – 100 Advanced & Numerical MCQs (MCQs 101–200)
MCQ No. 201
Two objects of different masses are dropped simultaneously from the same height in the absence of air resistance. Which statement is correct?
a. The heavier object reaches the ground first.
b. The lighter object reaches the ground first.
c. Both objects reach the ground at the same time.
d. The object with greater momentum reaches first.
Correct Answer: c. Both objects reach the ground at the same time.
Explanation:
In the absence of air resistance, all objects fall with the same acceleration due to gravity regardless of their masses. Although the heavier object has a greater weight, it also has proportionally greater inertia. Therefore, both objects take the same time to reach the ground.
MCQ No. 202
A car moves with constant speed around a circular track. Which statement is correct?
a. Its velocity remains constant.
b. No force acts on the car.
c. It is accelerating because its direction continuously changes.
d. Its momentum remains constant in both magnitude and direction.
Correct Answer: c. It is accelerating because its direction continuously changes.
Explanation:
Velocity is a vector quantity, so any change in its direction means a change in velocity. Therefore, even though the speed remains constant, the car has centripetal acceleration directed toward the center of the circular path.
MCQ No. 203
A ball is thrown vertically upward. Which statement is true during its upward journey?
a. Its velocity and acceleration are both upward.
b. Its velocity is upward while acceleration is downward.
c. Both velocity and acceleration are downward.
d. Acceleration becomes zero at the highest point.
Correct Answer: b. Its velocity is upward while acceleration is downward.
Explanation:
While the ball moves upward, gravity acts continuously downward. As a result, the upward velocity decreases uniformly until it becomes zero at the highest point, but the downward acceleration due to gravity remains constant throughout the motion.
MCQ No. 204
A passenger jumps forward from a slowly moving bus. Why is it safer to continue running after landing?
a. Running increases body weight.
b. Running increases stopping time and reduces the impact force.
c. Running decreases inertia.
d. Running eliminates momentum instantly.
Correct Answer: b. Running increases stopping time and reduces the impact force.
Explanation:
The passenger already possesses forward momentum before landing. By continuing to run, the stopping time increases, reducing the force experienced according to the impulse-momentum principle.
MCQ No. 205
A rocket can move in outer space because:
a. Air pushes the rocket forward.
b. Gravity pushes the rocket upward.
c. Expelled gases produce an equal and opposite reaction force.
d. Space contains sufficient oxygen for combustion.
Correct Answer: c. Expelled gases produce an equal and opposite reaction force.
Explanation:
Rocket propulsion depends on Newton's Third Law rather than the presence of air. The gases expelled backward produce an equal and opposite force that propels the rocket forward, even in the vacuum of space.
MCQ No. 206
If the slope of a displacement-time graph is increasing with time, the object is:
a. Moving with constant velocity.
b. At rest.
c. Accelerating.
d. Moving with constant acceleration equal to zero.
Correct Answer: c. Accelerating.
Explanation:
The slope of a displacement-time graph represents velocity. If the slope increases continuously, the velocity is increasing with time, indicating positive acceleration.
MCQ No. 207
A cricketer moves his hands backward while catching a fast-moving ball. Which physical quantity changes because of this action?
a. Momentum of the ball
b. Weight of the ball
c. Time of impact
d. Mass of the ball
Correct Answer: c. Time of impact.
Explanation:
The ball's momentum must decrease to zero whether the hands move or not. By increasing the time over which this change occurs, the average force experienced by both the ball and the player is reduced.
MCQ No. 208
A body is moving eastward. A force acts exactly westward. What will happen initially?
a. The speed increases.
b. The speed decreases.
c. The body immediately moves westward.
d. The acceleration becomes zero.
Correct Answer: b. The speed decreases.
Explanation:
The force acts opposite to the direction of motion, producing a negative acceleration. The body first slows down to rest before it can reverse its direction.
MCQ No. 209
Why does a projectile follow a curved path instead of a straight line?
a. Gravity acts only horizontally.
b. The horizontal velocity changes continuously.
c. Horizontal motion combines with vertically accelerated motion.
d. Air always bends its path.
Correct Answer: c. Horizontal motion combines with vertically accelerated motion.
Explanation:
The projectile moves with constant horizontal velocity while gravity continuously accelerates it downward. The combination of these two independent motions produces a parabolic trajectory.
MCQ No. 210
A person standing inside a lift feels lighter when the lift accelerates downward because:
a. His mass decreases.
b. Gravity becomes weaker.
c. The normal reaction force decreases.
d. His weight becomes zero.
Correct Answer: c. The normal reaction force decreases.
Explanation:
The actual weight of the person remains constant, but the apparent weight depends on the normal reaction exerted by the floor. During downward acceleration, this reaction force becomes smaller, making the person feel lighter.
MCQ No. 211
Two identical balls are thrown from the same height with equal speeds. One is thrown horizontally, while the other is dropped vertically. Neglecting air resistance, which reaches the ground first?
a. The horizontally thrown ball.
b. The vertically dropped ball.
c. Both reach simultaneously.
d. Cannot be determined.
Correct Answer: c. Both reach simultaneously.
Explanation:
The horizontal motion has no effect on the vertical motion. Since both balls have identical vertical motion under gravity, they reach the ground at the same time.
MCQ No. 212
Which graph represents an object moving with constant velocity?
a. A curved displacement-time graph.
b. A horizontal velocity-time graph.
c. A sloping acceleration-time graph.
d. A curved velocity-time graph.
Correct Answer: b. A horizontal velocity-time graph.
Explanation:
A horizontal line on a velocity-time graph indicates that the velocity remains unchanged with time. Since acceleration is zero, the object moves with constant velocity.
MCQ No. 213
Which quantity remains unchanged during the flight of a projectile in the absence of air resistance?
a. Resultant velocity
b. Vertical velocity
c. Horizontal component of velocity
d. Direction of motion
Correct Answer: c. Horizontal component of velocity.
Explanation:
Gravity acts only in the vertical direction. Since no horizontal force acts on the projectile, its horizontal component of velocity remains constant throughout the flight.
MCQ No. 214
When a fast-moving truck collides with a small car, the force exerted by the truck on the car is:
a. Greater than the force exerted by the car.
b. Smaller than the force exerted by the car.
c. Equal in magnitude to the force exerted by the car.
d. Zero because the truck is heavier.
Correct Answer: c. Equal in magnitude to the force exerted by the car.
Explanation:
According to Newton's Third Law, interaction forces always occur in equal and opposite pairs. Although the car experiences a much greater acceleration because of its smaller mass, the forces acting on both vehicles are equal in magnitude.
MCQ No. 215
If the net external force on an object is zero, which statement must be true?
a. The object is at rest only.
b. The object must move with constant speed in a straight line or remain at rest.
c. The object has zero momentum.
d. The object has zero mass.
Correct Answer: b. The object must move with constant speed in a straight line or remain at rest.
Explanation:
Newton's First Law states that when the resultant external force is zero, there is no acceleration. Therefore, the object either remains at rest or continues moving with constant velocity in a straight line.
MCQ No. 216
Which statement best explains why seat belts reduce injuries during sudden stops?
a. They reduce the passenger's momentum.
b. They increase the stopping time.
c. They reduce the passenger's mass.
d. They eliminate inertia.
Correct Answer: b. They increase the stopping time.
Explanation:
Seat belts allow the passenger to come to rest over a slightly longer time interval. According to the impulse-momentum relationship, increasing the stopping time reduces the average impact force.
MCQ No. 217
A projectile is launched at an angle greater than 45° while keeping the initial speed constant. Compared with 45°, its:
a. Range increases.
b. Maximum height increases but range decreases.
c. Time of flight decreases.
d. Horizontal velocity increases.
Correct Answer: b. Maximum height increases but range decreases.
Explanation:
A larger launch angle increases the vertical component of velocity, allowing the projectile to rise higher and remain in the air longer. However, the horizontal component decreases, reducing the horizontal range.
MCQ No. 218
An astronaut throws a tool forward while floating freely in space. The astronaut moves backward because of:
a. Newton's First Law.
b. Newton's Second Law.
c. Newton's Third Law and conservation of momentum.
d. Universal gravitation.
Correct Answer: c. Newton's Third Law and conservation of momentum.
Explanation:
When the tool is thrown forward, it gains forward momentum. To conserve the total momentum of the astronaut-tool system, the astronaut acquires an equal amount of momentum in the opposite direction.
MCQ No. 219
Which physical quantity is represented by the slope of a momentum-time graph?
a. Impulse
b. Force
c. Velocity
d. Acceleration
Correct Answer: b. Force.
Explanation:
Newton's Second Law states that force equals the rate of change of momentum (F = dp/dt). Therefore, the slope of a momentum-time graph represents the applied force.
MCQ No. 220
A body moves with constant speed but changing direction. Which statement is correct?
a. Its velocity is constant.
b. Its acceleration is zero.
c. It experiences a net force.
d. Its momentum remains unchanged.
Correct Answer: c. It experiences a net force.
Explanation:
A change in direction means the velocity is changing, even if the speed is constant. According to Newton's Second Law, a change in velocity requires acceleration, which in turn requires a net external force.
MCQ No. 221
In a perfectly elastic collision, which statement is true?
a. Only momentum is conserved.
b. Only kinetic energy is conserved.
c. Both momentum and kinetic energy are conserved.
d. Neither momentum nor kinetic energy is conserved.
Correct Answer: c. Both momentum and kinetic energy are conserved.
Explanation:
A perfectly elastic collision conserves both the total momentum and the total kinetic energy of the system. This ideal situation is approximately observed in collisions between molecules and some hard objects.
MCQ No. 222
Why is the stopping distance of a vehicle greater on a wet road?
a. Gravity increases.
b. Vehicle mass decreases.
c. Friction between the tyres and the road decreases.
d. Momentum becomes zero.
Correct Answer: c. Friction between the tyres and the road decreases.
Explanation:
Wet roads reduce the frictional force available between the tyres and the road surface. As a result, the braking force decreases, causing the vehicle to travel a longer distance before coming to rest.
MCQ No. 223
A ball thrown upward returns to the thrower's hand with the same speed (neglecting air resistance). Which quantity has changed?
a. Mass only
b. Speed only
c. Velocity
d. Acceleration due to gravity
Correct Answer: c. Velocity.
Explanation:
Although the speed is the same, the direction of motion is opposite when the ball returns. Since velocity depends on both magnitude and direction, the velocity has changed.
MCQ No. 224
Which of the following best demonstrates the conservation of momentum?
a. A satellite orbiting the Earth.
b. A rocket launching into space.
c. The recoil of a gun after firing a bullet.
d. A stone falling freely.
Correct Answer: c. The recoil of a gun after firing a bullet.
Explanation:
Initially, the total momentum of the gun-bullet system is zero. After firing, the forward momentum of the bullet is balanced by the backward momentum of the gun, ensuring that the total momentum remains conserved.
MCQ No. 225
Which statement best explains why Newton's Laws are considered approximations rather than exact laws?
a. They apply only on Earth.
b. They fail for moving vehicles.
c. They become inaccurate for objects moving close to the speed of light or at the quantum scale.
d. They are valid only for stationary objects.
Correct Answer: c. They become inaccurate for objects moving close to the speed of light or at the quantum scale.
Explanation:
Newton's Laws accurately describe most everyday phenomena and engineering applications. However, at extremely high speeds, Einstein's theory of relativity is required, and at atomic and subatomic scales, quantum mechanics provides a more accurate description.
MCQ No. 226
A passenger standing in a bus is thrown toward the left when the bus suddenly turns right. This happens because:
a. A force pushes the passenger to the left.
b. The passenger's body tends to continue moving in a straight line due to inertia.
c. Gravity acts toward the left.
d. The bus exerts an equal force on the passenger.
Correct Answer: b. The passenger's body tends to continue moving in a straight line due to inertia.
Explanation:
According to Newton's First Law, a body resists any change in its state of motion. When the bus turns right, the passenger's body tends to continue moving along its original straight-line path, making the passenger appear to move toward the left relative to the bus.
MCQ No. 227
A projectile is launched with a certain speed at 45°. If the launch speed is doubled while keeping the angle unchanged, the maximum height becomes:
a. Double
b. Three times
c. Four times
d. Eight times
Correct Answer: c. Four times
Explanation:
The maximum height of a projectile is proportional to the square of its initial speed (H ∝ u²). Therefore, doubling the launch speed increases the maximum height by a factor of 4.
MCQ No. 228
A body moves with constant speed along a circular path. Which statement is correct?
a. Both speed and velocity remain constant.
b. Its momentum remains constant in magnitude and direction.
c. Its kinetic energy remains constant, but its momentum continuously changes direction.
d. No force acts on the body.
Correct Answer: c. Its kinetic energy remains constant, but its momentum continuously changes direction.
Explanation:
Since the speed remains constant, the kinetic energy also remains constant. However, momentum is a vector quantity, so its direction changes continuously along the circular path, requiring a centripetal force.
MCQ No. 229
Which graph represents an object moving with uniform acceleration?
a. A curved velocity-time graph.
b. A straight-line velocity-time graph with constant slope.
c. A horizontal displacement-time graph.
d. A curved acceleration-time graph.
Correct Answer: b. A straight-line velocity-time graph with constant slope.
Explanation:
The slope of a velocity-time graph represents acceleration. A straight line with a constant slope indicates that the acceleration remains constant throughout the motion.
MCQ No. 230
Two identical balls are projected horizontally from the same height. One has twice the horizontal speed of the other. Which statement is correct?
a. The faster ball reaches the ground first.
b. The slower ball reaches the ground first.
c. Both reach the ground at the same time.
d. Their time of flight depends upon their masses.
Correct Answer: c. Both reach the ground at the same time.
Explanation:
The vertical motion of a projectile is completely independent of its horizontal motion. Since both balls start from the same height with the same vertical velocity (zero), they take the same time to reach the ground.
MCQ No. 231
A car and a truck collide head-on. Which statement is correct?
a. The truck exerts a greater force on the car.
b. The car exerts a greater force on the truck.
c. Each exerts an equal and opposite force on the other.
d. The heavier vehicle experiences the greater acceleration.
Correct Answer: c. Each exerts an equal and opposite force on the other.
Explanation:
According to Newton's Third Law, interaction forces always occur in equal and opposite pairs. The lighter vehicle experiences greater acceleration because acceleration depends on mass, not because the force is larger.
MCQ No. 232
Which of the following would produce the greatest impulse on an object?
a. A small force acting briefly.
b. A large force acting briefly.
c. A moderate force acting for a long time.
d. The largest product of force and time.
Correct Answer: d. The largest product of force and time.
Explanation:
Impulse equals Force × Time. Therefore, the greatest impulse is produced by whichever situation gives the largest value of the product F × t, regardless of whether the force or time alone is larger.
MCQ No. 233
If the slope of a displacement-time graph decreases with time, the object is:
a. Speeding up.
b. Moving with constant velocity.
c. Slowing down.
d. At rest throughout.
Correct Answer: c. Slowing down.
Explanation:
The slope of a displacement-time graph represents velocity. A decreasing slope means the velocity is becoming smaller with time, indicating that the object is slowing down.
MCQ No. 234
A ball rebounds from a wall with nearly the same speed. Compared with stopping at the wall, the rebound produces:
a. A smaller change in momentum.
b. The same change in momentum.
c. A larger change in momentum.
d. Zero change in momentum.
Correct Answer: c. A larger change in momentum.
Explanation:
When the ball rebounds, its momentum reverses direction instead of simply becoming zero. This reversal produces a greater change in momentum and therefore a greater impulse.
MCQ No. 235
An astronaut floating in deep space throws two objects of equal mass in opposite directions with equal speeds simultaneously. The astronaut will:
a. Move forward.
b. Move backward.
c. Remain at rest.
d. Rotate only.
Correct Answer: c. Remain at rest.
Explanation:
The two thrown objects have equal and opposite momenta, so their total momentum is zero. Since the initial momentum of the system was also zero, the astronaut experiences no net recoil.
MCQ No. 236
Why is the launch angle of 45° considered special for projectile motion on level ground?
a. It gives the longest time of flight.
b. It gives the greatest maximum height.
c. It produces the maximum horizontal range.
d. It makes horizontal and vertical velocities equal throughout the motion.
Correct Answer: c. It produces the maximum horizontal range.
Explanation:
For projectiles launched and landing at the same level without air resistance, the horizontal range is greatest at 45° because the horizontal and vertical components of the initial velocity are optimally balanced.
MCQ No. 237
A body moves with constant velocity. Which graph correctly represents its acceleration?
a. A horizontal line above the time axis.
b. A horizontal line along the time axis (zero acceleration).
c. A straight line with positive slope.
d. A curved graph increasing with time.
Correct Answer: b. A horizontal line along the time axis (zero acceleration).
Explanation:
Since the velocity does not change, the acceleration remains zero throughout the motion. An acceleration-time graph is therefore a horizontal line on the time axis.
MCQ No. 238
A person pushes a heavy box, but it does not move. Which statement is correct?
a. No force is applied.
b. The applied force is balanced by an equal opposing force.
c. Newton's Laws do not apply.
d. The box has no weight.
Correct Answer: b. The applied force is balanced by an equal opposing force.
Explanation:
The applied force is opposed by static friction of equal magnitude. Since the resultant force is zero, the box remains at rest according to Newton's First Law.
MCQ No. 239
During a perfectly inelastic collision, which statement is correct?
a. Both momentum and kinetic energy remain constant.
b. Momentum is conserved, but kinetic energy decreases.
c. Kinetic energy increases.
d. Neither momentum nor kinetic energy is conserved.
Correct Answer: b. Momentum is conserved, but kinetic energy decreases.
Explanation:
In a perfectly inelastic collision, the colliding bodies stick together after impact. Momentum remains conserved because no external force acts, but some kinetic energy is transformed into heat, sound, or deformation.
MCQ No. 240
A graph of momentum versus time has a constant positive slope. This indicates that the object experiences:
a. Zero force.
b. Constant force.
c. Increasing force.
d. Variable acceleration only.
Correct Answer: b. Constant force.
Explanation:
The slope of a momentum-time graph equals the force (F = dp/dt). A constant positive slope therefore represents a constant force acting on the object.
MCQ No. 241
Why does a cyclist lean inward while taking a sharp turn?
a. To reduce weight.
b. To increase mass.
c. To provide the required centripetal force and maintain balance.
d. To reduce friction.
Correct Answer: c. To provide the required centripetal force and maintain balance.
Explanation:
Leaning inward helps align the resultant force toward the center of the turn. This provides the necessary centripetal force and prevents the cyclist from toppling outward.
MCQ No. 242
A body moving east has a momentum of 20 kg·m/s. After turning north without changing speed, its momentum:
a. Remains unchanged.
b. Becomes zero.
c. Changes direction only.
d. Changes magnitude only.
Correct Answer: c. Changes direction only.
Explanation:
Momentum is a vector quantity. Since the speed and mass remain unchanged, the magnitude of the momentum stays the same, but its direction changes from east to north.
MCQ No. 243
If air resistance is considered in projectile motion, the projectile will:
a. Travel farther than predicted.
b. Reach a greater height.
c. Have a shorter range and lower maximum height.
d. Move with constant speed.
Correct Answer: c. Have a shorter range and lower maximum height.
Explanation:
Air resistance opposes the motion of the projectile throughout its flight. As a result, both the horizontal and vertical components of velocity decrease more rapidly, reducing the maximum height and horizontal range.
MCQ No. 244
Which statement best explains why heavier vehicles require longer stopping distances?
a. They always move faster.
b. They possess greater momentum.
c. Gravity is stronger on them.
d. Their acceleration is always greater.
Correct Answer: b. They possess greater momentum.
Explanation:
Momentum depends on both mass and velocity. For the same speed, a heavier vehicle has greater momentum and therefore requires a larger impulse and generally a longer distance to stop safely.
MCQ No. 245
Two objects of unequal masses collide in an isolated system. Which statement is always true?
a. They experience unequal forces.
b. Their accelerations are equal.
c. The total momentum before and after the collision remains the same.
d. Their kinetic energies remain unchanged.
Correct Answer: c. The total momentum before and after the collision remains the same.
Explanation:
Regardless of the masses involved, the total momentum of an isolated system remains conserved during every collision. The individual momenta may change, but the vector sum remains constant.
MCQ No. 246
Which situation provides the best example of Newton's Second Law?
a. A passenger falls forward when a bus stops.
b. A heavier shopping cart requires more force to produce the same acceleration as a lighter one.
c. A swimmer moves forward by pushing water backward.
d. A satellite continues orbiting Earth.
Correct Answer: b. A heavier shopping cart requires more force to produce the same acceleration as a lighter one.
Explanation:
Newton's Second Law states F = ma. For the same acceleration, a larger mass requires a proportionally larger force, demonstrating the direct relationship between force and mass.
MCQ No. 247
A body moves with constant acceleration. Which statement is correct about its velocity-time graph?
a. It is always horizontal.
b. It is a straight line.
c. It is always a parabola.
d. It is always a circle.
Correct Answer: b. It is a straight line.
Explanation:
A constant acceleration means velocity changes uniformly with time. Therefore, the velocity-time graph is a straight line whose slope equals the acceleration.
MCQ No. 248
During a collision, why may kinetic energy decrease even though momentum remains conserved?
a. Momentum and kinetic energy are unrelated.
b. Some kinetic energy is transformed into heat, sound, and deformation.
c. Momentum is destroyed.
d. Gravity removes energy.
Correct Answer: b. Some kinetic energy is transformed into heat, sound, and deformation.
Explanation:
In inelastic collisions, kinetic energy is converted into other forms of energy such as heat, sound, and deformation. However, momentum remains conserved because the internal interaction forces occur in equal and opposite pairs.
MCQ No. 249
A projectile reaches its maximum height. Which quantity is not zero at that instant?
a. Vertical velocity
b. Horizontal velocity
c. Instantaneous speed
d. Acceleration due to gravity
Correct Answer: d. Acceleration due to gravity.
Explanation:
At the highest point, the vertical component of velocity becomes zero, but gravity continues to act downward with an acceleration of 9.8 m/s². If the projectile has a horizontal component of velocity, it also remains non-zero.
MCQ No. 250
Which statement best summarizes the relationship between Newton's Laws and the Law of Conservation of Momentum?
a. They are completely unrelated principles.
b. Conservation of momentum is a direct consequence of Newton's Second Law only.
c. Conservation of momentum arises from the interaction forces described by Newton's Third Law together with Newton's Second Law in an isolated system.
d. Conservation of momentum applies only when Newton's Laws fail.
Correct Answer: c. Conservation of momentum arises from the interaction forces described by Newton's Third Law together with Newton's Second Law in an isolated system.
Explanation:
Newton's Third Law ensures that interaction forces between two bodies are equal in magnitude and opposite in direction, while Newton's Second Law relates these forces to changes in momentum. Together, they show that in the absence of external forces, the total momentum of an isolated system remains constant.
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