A uniform rectangular body floats in water. Given: length = 3 m, width = 2 m, overall depth = 1 m. The observed depth of immersion is 0.6 m. Find the weight of the body (assume fresh water).

Introduction / Context:
Buoyancy tells us that a floating body displaces a volume of liquid whose weight equals the body's weight. This question checks understanding of Archimedes' principle and how to compute displaced volume from plan area and immersion depth, then convert that displaced water into weight using density * gravity.

Given Data / Assumptions:

• Length L = 3 m
• Width B = 2 m
• Overall depth (thickness) = 1 m (not directly needed for buoyancy at float)
• Immersion depth h = 0.6 m
• Fresh water density rho = 1000 kg/m^3
• g = 9.81 m/s^2

Concept / Approach:
For a floating body at rest, Weight of body W = Weight of displaced liquid. Displaced volume V = plan area * immersion depth. Then W = rho * g * V. Convert to kN by dividing by 1000.

Step-by-Step Solution:

Verification / Alternative check:
If g is rounded to 9.8, W ≈ 1000 * 9.8 * 3.6 = 35.28 kN, still ≈ 35.3 kN. Either way, the same option is selected.

Why Other Options Are Wrong:

• 3.53 kN: Off by a factor of 10; likely confusion between meters and centimeters or forgetting g.
• 33.3 kN: Underestimates g (using 9.25) or rounding volume incorrectly.
• None of these: Incorrect because 35.3 kN is attainable and correct.

Common Pitfalls:
Using overall depth of 1 m instead of immersion depth; forgetting to multiply by g; using mass (kg) instead of weight (N); mixing units when converting to kN.

Final Answer:
35.3 kN