A light floating platform of horizontal area 200 cm² floats in water. A coin of mass 100 g is gently placed on the platform without allowing water to enter it. The additional downward displacement of the platform is N mm. Find N.
Physics · Fluid Mechanics · pascal law and buoyant force
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Question

A light floating platform of horizontal area 200 cm² floats in water. A coin of mass 100 g is gently placed on the platform without allowing water to enter it. The additional downward displacement of the platform is N mm. Find N.

Physics · Fluid Mechanics · pascal law and buoyant force

G1 Physics · Accepted Answer

The coin adds an additional downward force equal to its weight. Therefore the platform must displace an additional volume of water whose mass is 0.100 kg. Extra displaced volume: ΔV = m/ρ(water) = 0.100/1000 = 1.0×10⁻⁴ m³. Platform area: A = 200 cm² = 0.020 m². Hence, Δh = ΔV/A = 1.0×10⁻⁴/0.020 = 5×10⁻³ m = 5 mm. Therefore, N = 5.