Learning Path
Question & Answer1
Understand Question2
Review Options3
Learn Explanation4
Explore TopicChoose the Best Answer
A
A ball rolling down a hill reaches the bottom in the shortest time possible.
B
A pendulum swinging back and forth due to gravitational force.
C
A car accelerating from rest to a maximum speed on a straight road.
D
A satellite orbiting Earth due to gravitational attraction.
Understanding the Answer
Let's break down why this is correct
Answer
The Principle of Least Action says that a particle moving from one point to another takes the path that makes the integral of its Lagrangian (kinetic minus potential energy) over time as small as possible. In practice, this means the trajectory satisfies the Euler‑Lagrange equations, which are derived by setting the variation of that action integral to zero. A simple illustration is a ball thrown upward: the ball follows a parabola that makes the action minimal, which is exactly the path predicted by Newton’s laws. Thus, the scenario where a ball follows a parabolic arc from launch to landing best demonstrates the principle.
Detailed Explanation
The ball rolls down the hill following the path that uses the least action, which means the system moves from start to finish in the most efficient way. Other options are incorrect because A pendulum swings back and forth because of gravity, but it does not choose a path that minimizes action between two points; A car accelerating from rest to a maximum speed is driven by a force that changes its speed, not by minimizing action between two states.
Key Concepts
Principle of Least Action
Newton's Laws
Energy Conservation
Topic
Classical Mechanics Principles
Difficulty
medium level question
Cognitive Level
understand
Practice Similar Questions
Test your understanding with related questions
1
Question 1Which of the following scenarios best illustrates the Principle of Least Action in classical mechanics?
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2
Question 2Which of the following statements correctly apply the principles of classical mechanics? Select all that apply.
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3
Question 3In a closed system, how does the Principle of Least Action relate to the motion of a particle under conservative forces?
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4
Question 4In classical mechanics, the behavior of a system can be described using the principle of _____, which states that the path taken by a system is the one that minimizes the action integral.
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5
Question 5Which of the following statements correctly apply the principles of classical mechanics? Select all that apply.
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6
Question 6In a closed system, how does the Principle of Least Action relate to the motion of a particle under conservative forces?
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7
Question 7In classical mechanics, the behavior of a system can be described using the principle of _____, which states that the path taken by a system is the one that minimizes the action integral.
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8
Question 8Which of the following scenarios best illustrates the law of demand?
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