Choose the correct statement:

Options

A. Every oscillatory motion is periodic in nature.
B. Every periodic motion is oscillatory in nature.
C. The motion of a pendulum bob is periodic in nature (within its small amplitude).
D. Both (a) and ( c)

Explanation

To solve the question, we need to evaluate the given statements regarding oscillatory and periodic motion. Let's analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding Oscillatory Motion**:
- Oscillatory motion is defined as the motion of an object that moves back and forth around a fixed point (mean position).
- Example: A pendulum swinging back and forth.

2. **Statement A**: "Every oscillatory motion is periodic in nature."
- Since oscillatory motion repeats itself in regular intervals, it is indeed periodic.
- Therefore, this statement is **correct**.

3. **Statement B**: "Every periodic motion is oscillatory."
- Periodic motion refers to any motion that repeats after a fixed interval of time.
- However, not all periodic motions are oscillatory. For example, a vehicle moving in a circular path is periodic but does not exhibit to-and-fro motion.
- Therefore, this statement is **incorrect**.

4. **Statement C**: "The motion of a pendulum bob is periodic in nature."
- A pendulum bob swings back and forth around its mean position in regular intervals, making its motion periodic.
- Thus, this statement is **correct**.

5. **Conclusion**:
- From our analysis, we find that statements A and C are correct, while statement B is incorrect.
- Therefore, the correct answer is option 4: "Both A and C".

### Final Answer:
The correct statements are A and C.

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