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Question

# A wooden cube just floats inside water with a 400 gm mass placed on it. When the mass is removed, the cube floats with its top surface 4 cm above the water level. What is the side of the cube?

A
6 cm
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B
8 cm
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C
10 cm
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D
12 cm
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Solution

## The correct option is C 10 cmLet L and d be the side of the cube and density of the cube respectively. Given, weight of block, W=400 gm In first case, weight of the cube+weight of mass = weight of water displaced (L3×d×g) + W = L3×ρ×g (L3×d×g) + 400g = L3×1×g L3×d = L3−400........(1) ∵ Density of water,ρ=1g/cm3 In second case, (L−4) part of cube remains in water weight of the cube= weight of water displaced (L3×d×g) = L2×(L−4)×ρ×g L3×d = L2×(L−4).......(2) From (1) and (2) equations, L3−400= L2×(L−4) −400= −4L2 L=10 cm

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