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 tied to a string over a frictionless pulley, we can follow these steps:

### Step 1: Identify the masses
Let:
- \( m_1 = 4 \, \text{kg} \) (mass on one side)
- \( m_2 = 6 \, \text{kg} \) (mass on the other side)

### Step 2: Write down the formula for acceleration
The formula for the acceleration \( a \) of the system when two masses are connected by a string over a pulley is given by:
\[ a = \frac{m_2 - m_1}{m_1 + m_2} \cdot g \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

### Step 3: Substitute the values into the formula
Substituting the values of \( m_1 \) and \( m_2 \):
\[ a = \frac{6 \, \text{kg} - 4 \, \text{kg}}{4 \, \text{kg} + 6 \, \text{kg}} \cdot g \]

### Step 4: Simplify the expression
Calculating the numerator and denominator:
\[ a = \frac{2 \, \text{kg}}{10 \, \text{kg}} \cdot g \]
\[ a = \frac{1}{5} g \]

### Step 5: Conclusion
Thus, the acceleration of the system is:
\[ a = \frac{g}{5} \]