If three couples act on a body, the overall result is that
The correct answer and explanation is:
When three couples act on a body, the overall result is the sum of their individual moments (torques). To explain further, a couple refers to two equal and opposite forces that do not share a line of action, creating a rotational effect on an object. The magnitude of a couple is the product of the force and the perpendicular distance between the forces, and the direction of the couple is given by the right-hand rule.
Now, when three couples are applied to the same body, each couple will contribute its own moment, which can either enhance or oppose the other depending on their direction. The total effect on the body depends on the vector sum of the individual moments of the three couples. In other words, the moments from all three couples must be combined, keeping in mind the direction and magnitude of each moment.
However, one important point to note is that if the lines of action of the couples are parallel (or in the same plane), the body will experience a net rotational effect without any translational force. If the forces from the couples are arranged such that their directions do not cancel each other out, the body will rotate around the center of mass or axis of rotation influenced by the total moment.
On the other hand, if the three couples act in such a way that their moments cancel out (if the direction and magnitude of the moments oppose each other perfectly), there will be no net rotational effect. The body will remain in a state of equilibrium, and no rotation will occur.
In real-world applications, analyzing multiple couples acting on a body is essential for understanding mechanical systems like gears, levers, or any system subject to rotational forces. The result is a balance of moments that can either lead to rotation or maintain equilibrium.