Check up the only correct statement in the following

Options

A. a body has a constant velocity and still it can have a varying speed
B. a body has a constant speed but it can have a varying velocity
C. a body having constant speed cannot have any acceleration
D. all of the above

Answer

To solve the question of identifying the only correct statement regarding speed and velocity, we will analyze each option step by step.

### Step 1: Analyze the First Statement
**Statement:** A body has constant velocity and still can have varying speed.

**Analysis:**
- Velocity is a vector quantity that has both magnitude and direction.
- If a body has constant velocity, it means both the magnitude (speed) and direction of the velocity vector are constant.
- Therefore, if the velocity is constant, the speed cannot vary.

**Conclusion:** This statement is **incorrect**.

### Step 2: Analyze the Second Statement
**Statement:** A body has constant speed but can have varying velocity.

**Analysis:**
- Constant speed means that the magnitude of the velocity is constant.
- However, velocity can vary if the direction of the velocity vector changes.
- A classic example is uniform circular motion, where an object moves in a circle at a constant speed but the direction of the velocity changes continuously.

**Conclusion:** This statement is **correct**.

### Step 3: Analyze the Third Statement
**Statement:** A body having constant speed cannot have acceleration.

**Analysis:**
- Acceleration is defined as the rate of change of velocity.
- A body can have constant speed but still experience acceleration if its direction changes.
- For example, in uniform circular motion, the speed is constant, but the direction of the velocity changes, resulting in centripetal acceleration.

**Conclusion:** This statement is **incorrect**.

### Step 4: Analyze the Fourth Statement
**Statement:** All of the above.

**Analysis:**
- Since the first and third statements are incorrect, the statement "All of the above" is also incorrect.

### Final Conclusion
The only correct statement is the second one: **A body has constant speed but can have varying velocity.**

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