(A)A horse cannot pull cart and run in empty space
( R) : The mutual action- reaction forces between the horse and cart get cancelled

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
C. (A) is true but ( R) is false
D. Both (A) and (R ) are false

Answer

To solve the question, we need to analyze the statements given and determine their validity based on the principles of physics, particularly Newton's laws of motion.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- A horse is attached to a cart. When the horse tries to pull the cart, it exerts a force on the cart. According to Newton's third law, the cart exerts an equal and opposite force on the horse.

2. **Action and Reaction Forces**:
- The action force is the force exerted by the horse on the cart (let's call it \( F_{horse \to cart} \)).
- The reaction force is the force exerted by the cart on the horse (let's call it \( F_{cart \to horse} \)).
- According to Newton's third law, these forces are equal in magnitude and opposite in direction: \( F_{horse \to cart} = -F_{cart \to horse} \).

3. **Movement in Empty Space**:
- In empty space, there is no frictional force acting on the horse. Friction is essential for the horse to push against the ground to gain forward motion.
- Without friction, the horse cannot exert a forward force on the ground, and hence cannot move forward to pull the cart.

4. **Conclusion on the Statements**:
- (A) The statement "A horse cannot pull cart and run in empty space" is true because the absence of friction means the horse cannot generate the necessary force to move.
- (R) The statement "The mutual action-reaction forces between the horse and cart get cancelled" is also true. However, this does not explain why the horse cannot pull the cart in empty space.

5. **Final Evaluation**:
- Both statements are true, but the reason (R) does not correctly explain the situation described in (A). The correct explanation is the absence of friction in empty space, which is crucial for the horse's movement.

### Final Answer:
- (A) is true.
- (R) is true, but it does not provide the correct explanation for (A).