Introduction:

When a cylindrical disk rolls on a flat surface without slip, the motion can be analyzed using the concept of instantaneous center of rotation. The instantaneous center of rotation is the point on the disk around which it appears to rotate instantaneously at any given moment. To determine the location of the instantaneous center of rotation, we need to consider the motion of the disk and the constraints imposed by the absence of slipping.

Explanation:

To understand the location of the instantaneous center of rotation, let's consider the different options provided and analyze each one:

a) Centre of disk:
The center of the disk cannot be the instantaneous center of rotation because if it were, the disk would not roll on the surface without slipping. The center of the disk moves with the same linear velocity as any other point on the disk, but it does not rotate about itself.

b) Contact point:
The contact point between the disk and the surface is not the instantaneous center of rotation either. If it were, the disk would be rotating about the point of contact, which would cause slipping. The contact point remains stationary during the rolling motion.

c) On the normal to the surface at the contact point:
The instantaneous center of rotation is located on the normal to the surface at the contact point. This means that the line passing through the instantaneous center of rotation and the contact point is perpendicular to the surface. This is because the point of contact is instantaneously at rest, and any other point on the disk moves in a circular path around the instantaneous center of rotation.

d) On the tangent to the surface:
The instantaneous center of rotation is not located on the tangent to the surface. If it were, the disk would be rotating about a point different from the point of contact, which would cause slipping.

Conclusion:

In conclusion, the correct answer is c) on the normal to the surface at the contact point. This is the point around which the cylindrical disk appears to rotate instantaneously when it rolls on a flat surface without slip. Understanding the concept of instantaneous center of rotation is crucial for analyzing the motion of rolling objects and determining their kinematic properties.