Centre of gravity and stability：練習問題

A uniform cylinder is placed on its curved side on a horizontal surface. When it is pushed slightly, it rolls to a new position and remains at rest. Which term describes the state of equilibrium of the cylinder?

The diagram shows a uniform triangular piece of cardboard suspended from a pin at one of its corners. In which position will the cardboard come to rest?

A toy is in stable equilibrium. If the toy is tilted slightly and then released, which of the following correctly describes the change in the height of its centre of gravity and the moment that acts on it?

Which of the following modifications will increase the stability of a tall table lamp?

State the definition of the centre of gravity of an object.

An empty plastic bottle and an identical bottle half-filled with water are both placed on a plank. As one end of the plank is slowly lifted, the empty bottle topples over first. Explain this observation by referring to the position of the centre of gravity.

A uniform solid cylinder of height \(h\) and diameter \(d\) is placed on a rough surface. The surface is gradually tilted until the cylinder is on the verge of toppling at an angle of \(45^{\circ}\). Determine the mathematical relationship between \(h\) and \(d\) and explain your reasoning.

The diagram shows a uniform rectangular block of weight \( 10\text{ N} \), height \( 20\text{ cm} \), and base width \( 8\text{ cm} \) resting on a rough plank. The plank is slowly tilted at one end until the block is on the verge of toppling.

(a) Define the centre of gravity of an object.
(b) State the distance of the centre of gravity of the block from its base when it is standing upright.
(c) Identify the two physical factors that determine the stability of an object.
(d) Explain why the block topples over once the plank is tilted beyond a certain angle, referring to the line of action of its weight.