(A) : To unscrew a rusted nut, we need a wrench with longer arm.
(R ) : Wrench with longer arm reduces the torque of the arm.

Options

A. Both (A) and (R ) are true and (R ) is the correct explanation of (A)
B. Both (A) and (R ) are true and (R ) is not the correct explanation of (A)
C. (A) is true but (R ) is false
D. Both (A) and (R ) are false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that to unscrew a rusted nut, we need a wrench with a longer arm.
- This is true because a longer arm increases the distance from the point of rotation (the nut) to where the force is applied.

2. **Understanding Torque**:
- Torque (τ) is defined as the rotational effect of a force applied at a distance from the pivot point.
- The formula for torque is given by:
\[ \tau = r \times F \]
where \( r \) is the distance from the pivot point to the point where the force is applied, and \( F \) is the force applied.

3. **Effect of Arm Length on Torque**:
- When using a wrench, if the arm length (r) is increased, the torque also increases, provided the force (F) applied remains constant.
- This means that a longer wrench arm allows for greater torque, which makes it easier to unscrew the nut.

4. **Understanding the Reason (R)**:
- The reason states that a wrench with a longer arm reduces the torque of the arm.
- This statement is false because, as explained, a longer arm actually increases the torque.

5. **Conclusion**:
- The assertion (A) is true: a longer wrench arm is beneficial for unscrewing a rusted nut.
- The reason (R) is false: a longer arm does not reduce torque; it increases it.

### Final Answer:
- The assertion (A) is true, and the reason (R) is false. Therefore, the correct option is that A is true and R is false.