A force of `10 N` gives a mass `m_(1)` an acceleration of `10m//s^(2)` and a mass `m_(2)` an acceleration of `20m//s^(2)` What acceleration would it give if both the masses are tid together ?

Explanation

To solve the problem, we need to find the acceleration of two masses tied together when a force of 10 N is applied. We will first determine the individual masses using the given accelerations and then find the combined acceleration.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Force (F) = 10 N
- Acceleration of mass \( m_1 \) (A1) = 10 m/s²
- Acceleration of mass \( m_2 \) (A2) = 20 m/s²

2. **Calculate Mass \( m_1 \):**
Using Newton's second law, \( F = m \cdot a \), we can rearrange it to find the mass:
\[ m_1 = \frac{F}{A_1} = \frac{10 \, \text{N}}{10 \, \text{m/s}^2} = 1 \, \text{kg} \]

3. **Calculate Mass \( m_2 \):**
Similarly, we calculate the second mass:
\[ m_2 = \frac{F}{A_2} = \frac{10 \, \text{N}}{20 \, \text{m/s}^2} = 0.5 \, \text{kg} \]

4. **Combine the Masses:**
When both masses are tied together, the total mass \( M \) is:
\[ M = m_1 + m_2 = 1 \, \text{kg} + 0.5 \, \text{kg} = 1.5 \, \text{kg} \]

5. **Calculate the Combined Acceleration:**
Now, we can find the acceleration \( A \) when both masses are tied together using the same force:
\[ A = \frac{F}{M} = \frac{10 \, \text{N}}{1.5 \, \text{kg}} = \frac{10}{1.5} \approx 6.67 \, \text{m/s}^2 \]

### Final Answer:
The acceleration when both masses are tied together is approximately \( 6.67 \, \text{m/s}^2 \).