Topic: Fluid Mechanics
A wooden plank (sp. gravity = 0.5) of 1m x 1m x 0.5 m floats in water with 1.5 kN load on it with 1m x 1m surface horizontal. The depth of plank lying below water surface shall be
- A. 0.178 m
- B. 0.250 m
- C. 0.403 m
- D. 0.5 m
Answer: C. 0.403 m
Explanation: For equilibrium, the buoyant force equals the total weight (weight of the wooden plank + load). Buoyant force = $\rho_{w} g V_{submerged} = 1000 \times 9.81 \times (1 \times 1 \times x)$. Total weight = $(\rho_{plank} \times V \times g) + 1.5 \text{ kN} = (500 \times 1 \times 1 \times 0.5 \times 9.81) + 1500 = 2452.5 + 1500 = 3952.5$ N. Equating the two: $9810 \times x = 3952.5$, which yields $x = 0.4029$ m.