Assertion : In rotational plus translational motion of a rigid body, different particles of the rigid body may have different velocities but they will have same accelerations
Reason : Translational motion of a particle is equivalent to the translation motion of a rigid body.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is fasle
D. If Assertion is false but Reason is true

Answer

To solve the given problem, we need to analyze the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states: "In rotational plus translational motion of a rigid body, different particles of the rigid body may have different velocities but they will have the same accelerations."

- In a rigid body undergoing both translational and rotational motion, different particles indeed can have different velocities due to their positions relative to the axis of rotation. For instance, particles further from the axis of rotation will have higher linear velocities compared to those closer to the axis.
- However, the assertion claims that they will have the same acceleration, which is incorrect. Different points on the rigid body will have different accelerations due to their rotational motion.

### Step 2: Understand the Reason
The reason states: "Translational motion of a particle is equivalent to the translational motion of a rigid body."

- This statement is true. The translational motion of a rigid body can be described as the motion of its center of mass. All particles in the rigid body will have a component of motion that corresponds to the motion of the center of mass.
- However, in addition to this translational motion, each particle also has a component of motion due to rotation about the center of mass.

### Step 3: Conclusion
Based on the analysis:
- The assertion is **false** because different particles can have different accelerations in a rigid body undergoing both translational and rotational motion.
- The reason is **true** because the translational motion of a particle is indeed equivalent to the translational motion of the entire rigid body.

### Final Answer
- Assertion: False
- Reason: True