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A cube of density 0.5 g/cc and side 10 cm floats in water inside a cylindrical beaker of base area 1500 cm². Placing a mass m on top of the cube raises the water level in the beaker by 2 mm. Find m.
- 200 g
- 250 g
- 300 g
- 350 g
Correct answer: 300 g
Solution
Adding mass m increases the displaced water volume by m/ρ_water. This extra submerged volume causes the free surface (annular area = beaker area minus block base) to rise by Δh. Equating the added displaced volume to the rise gives m = ρ_water * A_beaker * Δh = 1 g/cc * 1500 cm² * 0.2 cm = 300 g.
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