Final answer:
The centre of gravity of a thin hollow cone is located at one-fourth of the total height above the base, which contributes to the object's stability when it is placed on its base and can cause it to fall if placed on its tip and displaced.
Step-by-step explanation:
The centre of gravity of a thin hollow cone lies on the axis of symmetry at a height of one-fourth of the total height above the base. This conclusion is based on the principle that the center of gravity (or center of mass) is the point at which the mass of the body is considered to be concentrated for the purpose of analysis. In the case of a uniform thin hollow cone, this position can be determined by considering the distribution of mass and the symmetry of the shape.
It is important to note that the center of gravity for such an object does not depend on whether it is in equilibrium or if a force is applied to its sides. However, the position of the center of gravity affects the stability of the object. If the cone is placed on its base, a displacement will cause the center of gravity to remain over its base, allowing it to return to its original position. On the other hand, if the cone is placed on its tip and displaced, the center of gravity will drift from its base, creating a torque that accelerates it to the ground.