Support and Force

When a force is applied to an object, it can cause two types of motion: translation and rotation. The support that does not allow the rotation of its attached member is called a fixed support or a pin support. In this case, option 'A' is the correct answer.

Explanation:

Translation:
Translation refers to the linear motion of an object where all points on the object move in the same direction and by the same distance. When a force is applied to an object, it can cause the object to move in a straight line without any rotation. This type of motion is known as translation.

Rotation:
Rotation refers to the circular or angular motion of an object where different points on the object move in different directions and by different distances. When a force is applied to an object, it can cause the object to rotate around a fixed point or axis. This type of motion is known as rotation.

Fixed Support:
A fixed support is a type of support that does not allow the rotation of its attached member. It provides resistance to both translation and rotation. A fixed support can be represented by a pin or a hinge, which allows only vertical and horizontal forces to be transmitted but prevents any rotational movement.

Example:
Consider a beam supported at one end by a fixed support and subjected to a vertical force at the other end. The fixed support will prevent the rotation of the beam and only allow vertical translation. The beam will experience a vertical displacement without any rotation.

Therefore, a support that does not allow the rotation of its attached member is referred to as a fixed support or a pin support. This is the correct answer to the given question.