To find the acceleration of the second object, we can use Newton's second law of motion, which states that \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
First, we need to determine the constant force \( F \) acting on the first object (with mass 26 kg and acceleration 2 m/s²):
\[ F = m \cdot a = 26 , \text{kg} \cdot 2 , \text{m/s}^2 = 52 , \text{N} \]
Now that we know the force is 52 N, we can use this force to find the acceleration of the second object, which has a mass of 4 kg:
Using the same formula \( F = ma \), rearranging gives:
\[ a = \frac{F}{m} \]
Substituting in the values we have:
\[ a = \frac{52 , \text{N}}{4 , \text{kg}} = 13 , \text{m/s}^2 \]
Therefore, the acceleration of the 4 kg object when the same constant force acts upon it is:
\[ \boxed{13 , \text{m/s}^2} \]