Choose the incorrect statement about the coefficient of restitution

Options

A. it is defined as the ratio of relative velocity of separation to the relative velocity of approach
B. it is defined only for two bodies
C. it is defined for colliding parts of the body along the normal to the striking surface
D. while calculating the velocity of approach and separation we take the velocities of centre of mass of the bodies

Answer

To solve the question regarding the coefficient of restitution and identify the incorrect statement, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Coefficient of Restitution (e)**:
- The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two colliding bodies.
- Mathematically, it can be expressed as:
\[ e = \frac{\text{Velocity of separation}}{\text{Velocity of approach}} \]

2. **Evaluating the Statements**:
- **Statement 1**: "It is defined as the ratio of relative velocity of separation to the relative velocity of approach."
- This statement is **correct** as it accurately describes the definition of the coefficient of restitution.

- **Statement 2**: "It is defined only for two bodies."
- This statement is also **correct** because the coefficient of restitution is applicable to two bodies involved in a collision.

- **Statement 3**: "While calculating the velocity of approach and the velocity of separation, we take the velocities of the center of mass of the body."
- This statement is **incorrect**. When calculating the coefficient of restitution, we consider the velocities of the colliding bodies at the point of contact, not necessarily the center of mass.

- **Statement 4**: "The component of velocity along the normal to the colliding surface is used in the equation of e."
- This statement is **correct**. The velocities used in the calculation of e are the components of the velocities along the normal direction to the surface at the point of collision.

3. **Conclusion**:
- The incorrect statement about the coefficient of restitution is **Statement 3**.

### Final Answer:
The incorrect statement about the coefficient of restitution is: **"While calculating the velocity of approach and the velocity of separation, we take the velocities of the center of mass of the body."**

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