A pendulum is oscillaring on either side its rest position.The correct statement is:
A pendulum is oscillaring on either side its rest position.The correct statement is:
A
It has the maximum potential energy at its extreme position.
B
It has the maximum kinetic energy at its extreme position.
C
it has the maximum potential energy at its mean position.
D
The sum of its kinetic and potential energies remains constant throughout the motion.
Text Solution
AI Generated Solution
The correct Answer is:
To solve the question regarding the pendulum oscillating around its rest position, we will analyze the statements provided and determine which one is correct.
### Step 1: Understand the motion of a pendulum
A pendulum swings back and forth around a central rest position. As it moves, it converts energy between kinetic energy (due to its motion) and potential energy (due to its height above the lowest point).
### Step 2: Analyze the energy at different positions
1. **At the extreme positions** (the highest points of the swing):
- The pendulum has maximum potential energy because it is at its highest point.
- The kinetic energy is zero because the pendulum momentarily stops before changing direction.
2. **At the mean position** (the lowest point of the swing):
- The pendulum has maximum kinetic energy because it is moving the fastest at this point.
- The potential energy is zero because it is at the lowest height.
### Step 3: Evaluate the statements
1. **Maximum potential energy at extreme position**: This statement is **true**.
2. **Maximum kinetic energy at extreme position**: This statement is **false**.
3. **Maximum potential energy at mean position**: This statement is **false**.
4. **Sum of kinetic and potential energy remains constant**: This statement is **true** according to the law of conservation of mechanical energy.
### Step 4: Conclusion
The correct statements regarding the pendulum's motion are:
- It has maximum potential energy at its extreme position.
- The sum of the kinetic and potential energy remains constant throughout the motion.
However, since the question asks for the correct statement, the most comprehensive and relevant answer is: **The sum of the kinetic and potential energy remains constant throughout the motion.**
### Final Answer
The correct statement is: **The sum of the kinetic and potential energy remains constant throughout the motion.**
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