(A) : It is harder to open and shut the door if we apply force near the hinge.
(R ) : Torque due to a given force is maximum at hinge of the door.

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 1: Understanding the Assertion
The assertion states that "It is harder to open and shut the door if we apply force near the hinge."
- When we apply a force near the hinge, the distance (r) from the hinge (the axis of rotation) to the point where the force is applied is small.

### Step 2: Understanding Torque
Torque (τ) is defined as the product of the force (F) and the distance (r) from the axis of rotation to the point of force application:
\[ \tau = r \times F \]
- If r is small, then the torque will also be small, which means the rotational effect of the force is reduced.

### Step 3: Conclusion from the Assertion
Since the torque is less when the force is applied near the hinge, it becomes harder to open or shut the door. Therefore, the assertion (A) is **true**.

### Step 4: Understanding the Reason
The reason states that "Torque due to a given force is maximum at the hinge of the door."
- This statement is incorrect. The torque is maximum when the force is applied at the farthest point from the hinge (the edge of the door) because this maximizes the distance (r).

### Step 5: Conclusion from the Reason
Since the reason (R) is incorrect, we conclude that while the assertion (A) is true, the reason (R) is false.

### Final Conclusion
- The assertion (A) is true.
- The reason (R) is false.

Thus, the correct answer is that the assertion is true and the reason is false.

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