Problem 4 Buoyancy A lock of mass 30 kg and volume 0.025m² is allowed to sink in water as shown below. A cylindrical rod of mass 1.25 kg, 5 m long, and 25 cm² in cross-section is attached to the weight and to the wall. 1. What will the angle be for equilibrium? 2. If the mass M is released from the road at equilibrium, how much of the rod will remain submerged? 0.25 m 5 m M = 30 kg V=0.025 m³ Figure 4: Lock sinking in water is attached to a wall with the use of a cylindrical rod

Our ancestors found that by tying two or more circular logs together to form a raft instead of digging a hollow in each log, it would have a more stable platform to carry more weight and enabled them to migrate further across the oceans. The reasons for this added stability are: (i) It increases the metacentric height GM by increasing the height of metacenter M. (ii) It increases the metacentric radius BM. It enables a large shift of the centre of buoyancy B laterally to produce a strong restoring moment when it is tilted. (A) (i) and (ii) (B) (ii) and (iii) (C) (i) and (iii) (D) All of the above In flow of air past an aerofoil with velocity U, a viscous boundary layer is formed arising from the viscous effect on the surface of the aerofoil. Due to no-slip condition at the wall, the velocity at the wall is zero. Across the boundary layer, the relationship between the static pressure at the wall and that at the edge of boundary layer is given by: P> P P₁ = Pe P₂ P