The degree of freedom for the vertical guided roller is ________a)0b)1...
Vertical guided roller resists horizontal/axial force and bending moment. However, it cannot resist vertical forces as it slides down along the plane. Hence it has 1 degree of freedom.

The degree of freedom for the vertical guided roller is ________a)0b)1...
The degree of freedom for the vertical guided roller is 1.
Explanation:
A roller support allows for translation in only one direction, which is perpendicular to the axis of the roller. This means that the roller can move up and down vertically, but it cannot move horizontally or rotate. Therefore, it has only one degree of freedom.
Degree of freedom refers to the number of independent movements or rotations that a structure or mechanism can have. In the case of a roller support, it can only move vertically, so it has a single degree of freedom.
To understand this concept further, let's consider the different types of supports commonly used in structural engineering:
1. Fixed Support: A fixed support provides complete restraint against translation and rotation in all directions. It has zero degrees of freedom.
2. Pinned Support: A pinned support allows for rotation but restricts translation in all directions. It has one degree of freedom.
3. Roller Support: A roller support allows for translation in one direction, perpendicular to the axis of the roller. It restricts translation in all other directions and rotation. It has one degree of freedom.
4. Hinged Support: A hinged support allows for rotation but restricts translation in all directions. It has one degree of freedom.
By understanding the characteristics of each type of support, we can determine the number of degrees of freedom for a given support condition. In the case of the vertical guided roller, it can only move vertically, so it has a single degree of freedom.
In conclusion, the correct answer is option B - 1 degree of freedom for the vertical guided roller.