Final answer:
The hand position that requires a smaller muscular force during push-ups is when the hands are 0.25 meters apart.
Step-by-step explanation:
When doing push-ups, the hand position that requires a smaller muscular force is when the hands are 0.25 meters apart. This is because when the hands are closer together, the lever arm (the horizontal distance between the hand and the elbow joint) is smaller, which reduces the torque required to perform the push-up. In comparison, when the hands are 0.5 meters apart, the lever arm is larger, resulting in a greater torque and requiring a larger muscular force.