To determine the force exerted by the 7 kg bowling ball on the 4 kg bowling ball during their collision while they are both accelerating at \(1.875 , \text{m/s}^2\), we can use Newton's second law of motion:
\[ F = ma \]
Where:
- \( F \) is the force,
- \( m \) is the mass of the object,
- \( a \) is the acceleration.
Using this for the 7 kg ball, we get:
\[ F = (7 , \text{kg})(1.875 , \text{m/s}^2) = 13.125 , \text{N} \]
Since the 7 kg ball is rolling to the right and exerting this force on the 4 kg ball (which is rolling to the left), this force would be considered as acting to the right.
Therefore, the answer is:
13.125 N to the right.