A solid cylinder is lifted out of oil by a wire attached to a motor. Fig. 5.1 shows two different positions X and Y of the cylinder during the lifting process. [Figure 5.1] The motor is fixed to an overhead beam. The cylinder has cross-sectional area 0.018m², length 1.2m and weight 560 N. The density of the oil is 940kgm⁻³. Throughout the lifting process, the cylinder moves vertically upwards with a constant velocity of 0.020 m s⁻¹. The viscous force of the oil acting on the cylinder is negligible.

1. (a)Calculate the density of the cylinder.[2]
2. (b)For the cylinder at position X, show that the upthrust due to the oil is 200 N.[2]
3. (c)(i)Calculate, for the moving cylinder at position X, the tension in the wire,[1]
4. (c)(ii)the power output of the motor.[2]
5. (d)(i)The cylinder is raised with constant velocity from position X to position Y. State and explain the variation, if any, of the power output of the motor as the cylinder is raised. Numerical values are not required.[3]
6. (d)(ii)The rate of energy output of the motor is less than the rate of increase of gravitational potential energy of the cylinder. Without calculation, explain this difference.[1]

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