A couple produces:

• (A). No motion
• (B). Linear and rotational motion
• (C). Purely rotational motion
• (D). Purely linear motion

When we talk about the types of motion produced by a couple, it's essential to understand what a couple is in the context of physics. A couple consists of two equal and opposite forces that act on an object but do not produce any translational motion. Instead, they create a rotational effect. Let's break down the options you've provided to clarify which type of motion a couple produces.

Understanding Couples in Physics

A couple is defined as two forces that are equal in magnitude, opposite in direction, and separated by a distance. This arrangement leads to a net torque but no net force. The key characteristic of a couple is that it causes an object to rotate around an axis without translating it in space.

Evaluating the Options

• No motion: This option suggests that there is no movement at all. However, since a couple generates torque, it will always produce some form of motion, specifically rotational motion.
• Linear and rotational motion: While a couple does create rotational motion, it does not produce linear motion. The forces cancel each other out, resulting in no net force to cause linear movement.
• Purely rotational motion: This is the correct answer. A couple generates torque, which leads to rotation around an axis without causing any linear displacement.
• Purely linear motion: Similar to the previous points, a couple does not produce linear motion because the forces are balanced and do not result in a net force acting on the object.

Conclusion on Motion Types

From this analysis, we can conclude that the correct answer is (C) Purely rotational motion. A couple effectively causes an object to rotate around a pivot point, making it a fundamental concept in mechanics, especially in understanding how forces interact in systems like gears, wheels, and levers.

Real-World Examples

To visualize this, think about a door handle. When you turn the handle, you apply a force at one end while the door's hinge acts as the pivot point. The forces you apply create a couple that allows the door to rotate open or closed without moving linearly in space.

In summary, a couple produces purely rotational motion, making it a crucial concept in understanding rotational dynamics in various physical systems.