A cylinder is made from a material of density 2.7 g cm⁻³. The cylinder has diameter 2.4 cm and length 5.0 cm. Show that the cylinder has weight 0.60 N.

1. (a)A cylinder is made from a material of density 2.7 g cm⁻³. The cylinder has diameter 2.4 cm and length 5.0 cm. Show that the cylinder has weight 0.60 N.[3]
2. (b)The cylinder in (a) is hung from the end A of a non-uniform bar AB, as shown in Fig. 3.1. [Figure 3.1] The bar has length 50 cm and has weight 0.25 N. The centre of gravity of the bar is 20 cm from B. The bar is pivoted at P. The pivot is 12 cm from B. An object X is hung from end B. The weight of X is adjusted until the bar is horizontal and in equilibrium.
3. (b)(i)Explain what is meant by centre of gravity.[1]
4. (b)(ii)Calculate the weight of X.[3]
5. (c)The cylinder is now immersed in water, as illustrated in Fig. 3.2. [Figure 3.2] An upthrust acts on the cylinder and the bar is not in equilibrium.
6. (c)(i)Explain the origin of the upthrust.[2]
7. (c)(ii)Explain why the weight of X must be reduced in order to obtain equilibrium for AB.[1]

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