The center of mass of a system consisting of two spheres is moving in the positive x direction with a speed of 5.0 m/s. One sphere has a mass of 2.5 kg and the other has a mass of 3.5 kg. The total momentum of the system is :

Options

A. 0
B. `(5.0 kg m//s) hati`
C. `(12.5 kg m//s) hati`
D. `(30 kg m//s) hati`

Explanation

To find the total momentum of the system consisting of two spheres, we can follow these steps:

### Step 1: Identify the masses and the velocity of the center of mass
- Mass of the first sphere (m1) = 2.5 kg
- Mass of the second sphere (m2) = 3.5 kg
- Velocity of the center of mass (v_cm) = 5.0 m/s in the positive x direction

### Step 2: Calculate the total mass of the system
The total mass (M) of the system is the sum of the masses of the two spheres:
\[ M = m_1 + m_2 = 2.5 \, \text{kg} + 3.5 \, \text{kg} = 6.0 \, \text{kg} \]

### Step 3: Use the formula for momentum
The total momentum (P) of the system can be calculated using the formula:
\[ P = M \cdot v_{cm} \]
Substituting the values we have:
\[ P = 6.0 \, \text{kg} \cdot 5.0 \, \text{m/s} \]

### Step 4: Calculate the total momentum
Now, we perform the multiplication:
\[ P = 30.0 \, \text{kg m/s} \]

### Final Answer
The total momentum of the system is:
\[ P = 30.0 \, \text{kg m/s} \]

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