A pendulum consists of a solid sphere suspended by a string from a fixed point P, as shown in Fig. 3.1. [Figure 3.1] The sphere swings from side to side. At one instant the sphere is at its lowest position X, where it has kinetic energy 0.86 J and momentum 0.72 Ns in a horizontal direction. A short time later the sphere is at position Y, where it is momentarily stationary at a maximum vertical height h above position X. The string has a fixed length and negligible weight. Air resistance is also negligible.

1. (a)On Fig. 3.1, draw a solid line to represent the displacement of the centre of the sphere at position Y from position X.[1]
2. (b)Show that the mass of the sphere is 0.30 kg.[3]
3. (c)Calculate height h.[2]
4. (d)The distance between point P and the centre of the sphere is 0.93 m. When the sphere is at position Y, the string is at an angle θ to the vertical. Show that θ is 47°.[1]
5. (e)For the sphere at position Y, calculate the moment of its weight about point P.[2]
6. (f)State and explain whether the sphere is in equilibrium when it is stationary at position Y.[1]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.