Check up only the 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 is can have a varying velocity
C. a body has a constant speed cannot have any acceleration
D. a body in motion under a force acting upon it must always have work done upon it

Answer

To solve the question, we need to analyze the four statements provided and determine which one is correct. Let's go through each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** A body has a constant velocity but still can have a varying speed.

- **Explanation:** Velocity is a vector quantity that includes both magnitude and direction. If a body has a constant velocity, both its speed (magnitude) and direction must remain constant. Therefore, it is impossible for a body to have a constant velocity and at the same time have a varying speed.
- **Conclusion:** This statement is **incorrect**.

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

- **Explanation:** This statement can be true in the case of uniform circular motion (UCM). In UCM, an object moves in a circular path with a constant speed, but the direction of the velocity vector changes continuously. Since velocity is a vector, a change in direction means that the velocity is varying, even though the speed remains constant.
- **Conclusion:** This statement is **correct**.

### Step 3: Analyze Statement 3
**Statement 3:** A body with a constant speed cannot have an acceleration.

- **Explanation:** This statement is incorrect. In uniform circular motion, while the speed remains constant, the direction of the velocity changes, which means there is an acceleration (centripetal acceleration) acting towards the center of the circular path. Thus, a body can have a constant speed and still experience acceleration.
- **Conclusion:** This statement is **incorrect**.

### Step 4: Analyze Statement 4
**Statement 4:** A body in motion under a force acting upon it must always have work done upon it.

- **Explanation:** This statement is also incorrect. In circular motion, the force acting on the body (centripetal force) is directed towards the center of the circle, while the displacement is tangential to the circular path. The angle between the force and displacement is 90 degrees, which means that the work done is zero (since work done = Force × Displacement × cos(θ) and cos(90°) = 0).
- **Conclusion:** This statement is **incorrect**.

### Final Conclusion
After analyzing all four statements, we find that the only correct statement is **Statement 2**: "A body has constant speed but can have a varying velocity."

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