Statement A : If the force varies with time in a complicated way then the average force is measured by the total change in momentum of the body
Statement B : Change in momentum and impulsive force are numerically equal

Options

A. A and B are correct
B. A and B are false
C. A is true and B is false
D. A is false and B is true

Answer

To analyze the statements provided in the question, we will break down the concepts of force, momentum, and impulse step by step.

### Step 1: Understanding Statement A
Statement A claims that if the force varies with time in a complicated way, then the average force is measured by the total change in momentum of the body.

1. **Force and Momentum Relation**:
- The force (F) acting on an object is related to its momentum (p) by the equation:
\[ F = \frac{dp}{dt} \]
- Here, \( dp \) is the change in momentum and \( dt \) is the change in time.

2. **Average Force**:
- The average force over a time interval can be expressed as:
\[ F_{avg} = \frac{\Delta p}{\Delta t} \]
- Where \( \Delta p \) is the total change in momentum over the time interval \( \Delta t \).

3. **Conclusion for Statement A**:
- While the average force is related to the total change in momentum, it is important to note that it also depends on the time interval. Therefore, Statement A is **incorrect** as it does not mention the time factor.

### Step 2: Understanding Statement B
Statement B states that the change in momentum and impulsive force are numerically equal.

1. **Impulse**:
- Impulse (J) is defined as the product of force and the time duration over which the force acts:
\[ J = F \cdot \Delta t \]

2. **Change in Momentum**:
- According to the impulse-momentum theorem, the impulse experienced by an object is equal to the change in momentum of that object:
\[ J = \Delta p \]
- This means that the impulse applied to an object results in a change in its momentum.

3. **Conclusion for Statement B**:
- Since impulse is equal to the change in momentum, Statement B is **correct**.

### Final Conclusion
- Statement A is **false** because it does not account for the time factor in defining average force.
- Statement B is **true** because it correctly states that change in momentum is equal to the impulse applied.

### Answer
- **Statement A**: False
- **Statement B**: True