(A) : It is easier to pull a lawn roller than to push on the same horizontal rough surface
(R ) : Pulling body decreases normal reaction

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: "It is easier to pull a lawn roller than to push it on the same horizontal rough surface."
- This can be understood by considering the forces acting on the lawn roller when it is pulled versus when it is pushed.

2. **Forces Acting When Pushing**:
- When the lawn roller is pushed, the applied force (F) has two components:
- A horizontal component: \( F \cos \theta \)
- A vertical component: \( F \sin \theta \) (acting downwards)
- The normal force (N) acting on the roller when pushed is given by:
\[ N = mg + F \sin \theta \]
- Here, \( mg \) is the weight of the roller.

3. **Frictional Force When Pushing**:
- The frictional force (f) opposing the motion is given by:
\[ f = \mu N = \mu (mg + F \sin \theta) \]
- This indicates that the frictional force is higher when pushing because the normal force is increased by the vertical component of the applied force.

4. **Forces Acting When Pulling**:
- When the lawn roller is pulled, the applied force (F) also has two components:
- A horizontal component: \( F \cos \theta \)
- A vertical component: \( F \sin \theta \) (acting upwards)
- The normal force (N) when pulling is given by:
\[ N = mg - F \sin \theta \]
- The vertical component acts to reduce the normal force.

5. **Frictional Force When Pulling**:
- The frictional force (f) opposing the motion when pulling is given by:
\[ f = \mu N = \mu (mg - F \sin \theta) \]
- This indicates that the frictional force is lower when pulling because the normal force is decreased by the vertical component of the applied force.

6. **Conclusion**:
- Since the frictional force is lower when pulling than when pushing, it is indeed easier to pull the lawn roller than to push it.
- Therefore, the assertion (A) is true.

7. **Analyzing the Reason (R)**:
- The reason states: "Pulling body decreases normal reaction."
- This is also true, as we derived that the normal force is reduced when pulling due to the upward vertical component of the pulling force.
- Thus, the reason (R) correctly explains the assertion (A).

### Final Answer:
Both the assertion (A) and the reason (R) are true, and R is the correct explanation of A.