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 determine which of the sentences regarding momentum are correct, let's analyze each option step by step.

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

**Explanation:**
Momentum (denoted as \( p \)) is defined as the product of mass (\( m \)) and velocity (\( v \)). Mathematically, it is expressed as:
\[ p = m \cdot v \]
Since velocity is a vector quantity (it has both magnitude and direction), momentum is also a vector quantity. Therefore, this statement is correct.

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

**Explanation:**
As established earlier, momentum is derived from mass (a scalar) and velocity (a vector). Since momentum retains the vector nature of velocity, it is not a scalar quantity. Thus, this statement is incorrect.

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

**Explanation:**
The rate of change of momentum is defined as:
\[ \frac{dP}{dt} = F \]
where \( F \) is the force acting on the object. According to Newton's second law, the force is equal to the rate of change of momentum, and it acts in the same direction as the applied force. Therefore, this statement is correct.

### Step 4: Analyze Option 4
**Statement:** "Both 1 and 3 are correct."

**Explanation:**
Since we have established that both Option 1 and Option 3 are correct, this statement is also correct.

### Conclusion
Based on the analysis:
- Option 1 is correct.
- Option 2 is incorrect.
- Option 3 is correct.
- Option 4 is correct.

Thus, the correct answer is **Option 4**: Both 1 and 3 are correct.

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