Which of the following statements is wrong

Options

A. If speed of a particle changes, its velocity must change.
B. If velocity of a particle doesn’t change, its speed must remain constant
C. If speed of a particle doesn’t change, its velocity must remain constant
D. If velocity of a particle changes , its speed may or may not change

Explanation

To determine which statement is wrong, let's analyze each statement step by step:

### Step 1: Analyze Statement 1
**Statement 1:** If the speed of a particle changes, then its velocity must change.

- **Explanation:** Speed is the magnitude of velocity. If the speed changes, it means the magnitude of the velocity vector is changing. Since velocity is a vector quantity that includes both magnitude and direction, a change in speed implies a change in the velocity vector. Therefore, this statement is **correct**.

### Step 2: Analyze Statement 2
**Statement 2:** If the velocity of the particle doesn't change, then speed must remain constant.

- **Explanation:** If the velocity vector does not change, it means both its magnitude and direction are constant. Since speed is the magnitude of velocity, if velocity is constant, speed must also be constant. Therefore, this statement is **correct**.

### Step 3: Analyze Statement 3
**Statement 3:** If the speed of the particle does not change, then its velocity must remain constant.

- **Explanation:** Consider uniform circular motion as an example. In this case, the speed of the particle remains constant, but the direction of the velocity vector changes continuously. Therefore, even though the speed is constant, the velocity is not constant due to the changing direction. Thus, this statement is **incorrect**.

### Step 4: Analyze Statement 4
**Statement 4:** If the velocity of a particle changes, then its speed may or may not change.

- **Explanation:** In non-uniform circular motion, the velocity can change due to a change in direction and/or speed. However, it is possible for the speed to remain constant while the direction changes. Therefore, this statement is **correct**.

### Conclusion
The wrong statement among the options provided is **Statement 3**: "If the speed of the particle does not change, then its velocity must remain constant."

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