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, let's analyze each statement step by step.

### Step-by-Step Solution:

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

2. **Analyzing the Statements**:
- **Statement A**: "It is defined as the ratio of relative velocity of separation to relative velocity of approach."
- This statement is **true**. This is the fundamental definition of the coefficient of restitution.

- **Statement B**: "It is defined only for two bodies."
- This statement is also **true**. The coefficient of restitution applies specifically to the interaction between two colliding bodies.

- **Statement C**: "It is defined for colliding part of the body along the normal to the striking surface."
- This statement is **true**. The coefficient of restitution is concerned with the velocities at the point of contact, which is normal to the surface during the collision.

- **Statement D**: "While calculating the velocity of approach and separation we can take the velocity of center of mass of the body."
- This statement is **incorrect**. The velocities of approach and separation are determined at the point of contact, not at the center of mass of the bodies.

3. **Conclusion**:
The incorrect statement regarding the coefficient of restitution is **Statement D**.