Two bodies of masses 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a frictionless pulley. The acceleration of the system is `:`

Options

A. `( g)/( 2)`
B. `( g)/( 3)`
C. `( g)/( 5)`
D. `( g)/( 10) `

Answer

To find the acceleration of the system with two masses (4 kg and 6 kg) connected by a string over a frictionless pulley, we can follow these steps:

### Step 1: Identify the Forces Acting on Each Mass
- The mass \( m_1 = 4 \, \text{kg} \) will experience a gravitational force downward, which is \( F_{g1} = m_1 \cdot g = 4g \).
- The mass \( m_2 = 6 \, \text{kg} \) will also experience a gravitational force downward, which is \( F_{g2} = m_2 \cdot g = 6g \).

### Step 2: Determine the Net Force Acting on the System
Since the 6 kg mass is heavier, it will accelerate downward, while the 4 kg mass will accelerate upward. The net force acting on the system can be calculated as:
\[ F_{\text{net}} = F_{g2} - F_{g1} = 6g - 4g = 2g \]

### Step 3: Calculate the Total Mass of the System
The total mass \( m_{\text{total}} \) of the system is the sum of the two masses:
\[ m_{\text{total}} = m_1 + m_2 = 4 \, \text{kg} + 6 \, \text{kg} = 10 \, \text{kg} \]

### Step 4: Apply Newton's Second Law
According to Newton's second law, the acceleration \( a \) of the system can be found using the formula:
\[ F_{\text{net}} = m_{\text{total}} \cdot a \]
Substituting the values we have:
\[ 2g = 10a \]

### Step 5: Solve for Acceleration
To find \( a \), we rearrange the equation:
\[ a = \frac{2g}{10} = \frac{g}{5} \]

### Final Answer
Thus, the acceleration of the system is:
\[ a = \frac{g}{5} \, \text{m/s}^2 \]