Final answer:
The electric handpiece has the greatest torque, thanks to its motorized gearing, which allows it to outperform pneumatic, hydraulic, or manual handpieces under the same conditions.
Step-by-step explanation:
The handpiece that has the greatest torque is the electric handpiece. Torque is the turning or twisting effectiveness of a force. In addition to the magnitude of the force, the distance from the pivot point and the angle at which the force is applied also affects the torque. For all other factors being equal, such as the magnitude of force and the distance from the pivot point, an electric handpiece is typically designed to provide higher torque compared to pneumatic, hydraulic, or manual handpieces due to its motorized gearing and efficiency.
In the context of physics, when multiple forces of equal magnitude are applied to an object anchored at a point, the force that will provide the greatest torque is the one applied furthest from the pivot point and at a perpendicular angle (90°) to the lever arm. The formula for torque is T = rF sin p, where r is the lever arm's length, F is the force applied, and p is the angle between the force vector and the lever arm.