A spring is extended by a force. The variation with extension x of the force F is shown in Fig. 3.1. [Figure 3.1]

1. (a)State the name of the law that relates the force and extension of the spring shown in Fig. 3.1.[1]
2. (b)(i)Determine: (i) the spring constant, in Nm⁻¹, of the spring spring constant = ..................................................... Nm⁻¹[2]
3. (b)(ii)the strain energy (elastic potential energy) in the spring when the extension is 4.0 cm. strain energy = ..................................................... J[2]
4. (c)(i)One end of the spring is attached to a fixed point. A cylinder that is submerged in a liquid is now suspended from the other end of the spring, as shown in Fig. 3.2. [Figure 3.2] The cylinder has length 5.8cm, cross-sectional area 1.2 × 10⁻³m² and weight 6.20N. The cylinder is in equilibrium when the extension of the spring is 4.0 cm. (i) Show that the upthrust acting on the cylinder is 0.60N.[1]
5. (c)(ii)Calculate the difference in pressure between the bottom face and the top face of the cylinder. difference in pressure = ..................................................... Pa[2]
6. (c)(iii)Calculate the density of the liquid. density = ..................................................... kgm⁻³[2]
7. (d)(i)The liquid in (c) is replaced by another liquid of greater density. State the effect, if any, of this change on: (i) the upthrust acting on the cylinder[1]
8. (d)(ii)(ii) the extension of the spring.[1]

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