No, the acceleration of an object may differ depending on whether the force is applied through its center of mass or not, even if the magnitude of the force is the same. The location where the force is applied can have an impact on the resulting motion of the object.
If a force is applied through the center of mass of an object, it will cause the object to undergo linear acceleration without rotation. This is because the force acts directly along the line of motion and produces no torque or rotational effects.
However, if the force is applied off-center or at a different point on the object, it can create a torque or rotational force in addition to the linear force. This rotational force can cause the object to undergo both linear and rotational acceleration. The resulting motion will depend on the distribution of mass and the location where the force is applied.
In summary, the acceleration of an object can vary depending on whether the force is applied through its center of mass or not. If the force is applied through the center of mass, only linear acceleration occurs. If the force is applied off-center, both linear and rotational acceleration may occur.