which of the following sentence is/are correct

Options

A. momentum has both direction and magnitude
B. momentum is a scalar quantity
C. the rate of change of momentum of an object is in the direction of force
D. both (1) and (3)

Answer

To solve the question regarding which of the following sentences are correct, we will analyze each option step by step.

### Step 1: Analyze Option A
**Statement**: Momentum has both direction and magnitude.

**Explanation**:
- Momentum (P) is defined as the product of mass (m) and velocity (v): \( P = m \cdot v \).
- Since velocity is a vector quantity (it has both magnitude and direction), momentum, which is the product of a scalar (mass) and a vector (velocity), is also a vector quantity.
- Therefore, momentum indeed has both direction and magnitude.

**Conclusion**: Option A is correct.

### Step 2: Analyze Option B
**Statement**: Momentum is a scalar quantity.

**Explanation**:
- As established in Step 1, momentum is a vector quantity because it depends on velocity, which is a vector.
- Therefore, this statement is incorrect.

**Conclusion**: Option B is incorrect.

### Step 3: Analyze Option C
**Statement**: The rate of change of momentum of an object is in the direction of the force.

**Explanation**:
- According to Newton's second law, the force (F) acting on an object is equal to the rate of change of momentum (dp/dt): \( F = \frac{dp}{dt} \).
- This means that the direction of the force is the same as the direction of the change in momentum.
- Therefore, this statement is correct.

**Conclusion**: Option C is correct.

### Step 4: Compile the Results
- From the analysis:
- Option A is correct.
- Option B is incorrect.
- Option C is correct.

### Final Conclusion
- The correct options are A and C.
- Therefore, the final answer is that both statements 1 (A) and 3 (C) are correct.

### Answer:
The correct option is D: Both 1 and 3 are correct.

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