A force of `5N` gives a mass `m_(1)`, an acceleration of `m//s^(2)`, and a mass `m_(2)`, an acceleration of `24 m//s^(2)`. What acceleration would it give if both the masses are tied together?

Options

A. 5 m/s2
B. 10 m/s2
C. 6 m/s2
D. NOne

Explanation

To solve the problem step by step, we need to find the acceleration of the combined mass when both masses \( m_1 \) and \( m_2 \) are tied together and subjected to a force of \( 5N \).

### Step 1: Determine the mass \( m_1 \)
We know that the force \( F \) acting on mass \( m_1 \) produces an acceleration of \( 8 m/s^2 \). According to Newton's second law, we can write:
\[ F = m_1 \cdot a_1 \]
Substituting the known values:
\[ 5N = m_1 \cdot 8 m/s^2 \]
Now, we can solve for \( m_1 \):
\[ m_1 = \frac{5N}{8 m/s^2} = \frac{5}{8} \text{ kg} \]

### Step 2: Determine the mass \( m_2 \)
Similarly, for mass \( m_2 \) which has an acceleration of \( 24 m/s^2 \):
\[ F = m_2 \cdot a_2 \]
Substituting the known values:
\[ 5N = m_2 \cdot 24 m/s^2 \]
Now, we can solve for \( m_2 \):
\[ m_2 = \frac{5N}{24 m/s^2} = \frac{5}{24} \text{ kg} \]

### Step 3: Calculate the total mass \( m_1 + m_2 \)
Now that we have both masses, we can find the total mass:
\[ m_1 + m_2 = \frac{5}{8} \text{ kg} + \frac{5}{24} \text{ kg} \]
To add these fractions, we need a common denominator. The least common multiple of \( 8 \) and \( 24 \) is \( 24 \):
\[ m_1 = \frac{5}{8} = \frac{15}{24} \text{ kg} \]
Now we can add:
\[ m_1 + m_2 = \frac{15}{24} + \frac{5}{24} = \frac{20}{24} = \frac{5}{6} \text{ kg} \]

### Step 4: Calculate the acceleration of the combined mass
Now we can use the total mass and the force to find the acceleration when both masses are tied together:
\[ F = (m_1 + m_2) \cdot a \]
Substituting the known values:
\[ 5N = \left(\frac{5}{6} \text{ kg}\right) \cdot a \]
Solving for \( a \):
\[ a = \frac{5N}{\frac{5}{6} \text{ kg}} = 5N \cdot \frac{6}{5} = 6 m/s^2 \]

### Final Answer
The acceleration when both masses are tied together is:
\[ \boxed{6 \, m/s^2} \]