A judo fighter in order to throw his opponent on the mat tries to initially bend his opponent and then rotate him around his hip.
As the mass of the opponent is brought closer to the fighter's hip, the force required to throw the opponent is reduced.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion.
B. if both assertion and reason are true but reason is not the correct expalanation of the assertion
C. if assertion is true , but reason is false
D. both assertion and reason are false statements.

Explanation

To solve the problem, we need to analyze the actions of the judo fighter and the physics principles involved in throwing an opponent.

### Step-by-Step Solution:

1. **Understanding the Action**: The judo fighter bends his opponent and then rotates him around his hip. This action is crucial for effectively throwing the opponent.

**Hint**: Think about how bending affects the position of the opponent's center of mass.

2. **Center of Mass**: When the opponent is bent, their center of mass is brought closer to the fighter's hip. This is important because the hip acts as the pivot point for the rotation.

**Hint**: Consider how the distance from the pivot affects the torque.

3. **Torque Calculation**: Torque (\( \tau \)) is calculated as the product of the force (\( F \)) and the distance (\( r \)) from the pivot point: \( \tau = r \times F \). As the opponent's mass is brought closer to the hip, the distance \( r \) decreases.

**Hint**: Remember that a smaller distance means less torque is needed to achieve the same rotational effect.

4. **Moment of Inertia**: The moment of inertia (\( I \)) of the opponent about the hip decreases as their mass is brought closer. The moment of inertia is a measure of how difficult it is to rotate an object.

**Hint**: Reflect on how the distribution of mass affects the moment of inertia.

5. **Reduced Force Requirement**: With a smaller moment of inertia and reduced torque required, the force needed to throw the opponent decreases. This makes it easier for the fighter to execute the throw.

**Hint**: Think about how easier it is to rotate a lighter object compared to a heavier one.

6. **Conclusion**: Therefore, both the assertion (the fighter bends and rotates the opponent) and the reason (the force required is reduced as the mass is brought closer to the hip) are true. The reason correctly explains the assertion.

**Hint**: Summarize the relationship between torque, moment of inertia, and force in your conclusion.

### Final Answer:
Both the assertion and reason are true, and the reason is a correct explanation of the assertion. The fighter's technique effectively reduces the force required to throw the opponent by manipulating the opponent's center of mass and moment of inertia.