A wooden cube just floats inside water with a 200gm mass placed on it. When the mass is removed, the cube floats with its top surface 2cm above the water level. What is the side of the cube? [Take g=10m/s2]
A
6cm
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B
8cm
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C
10cm
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D
12cm
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Solution
The correct option is C10cm Let the side of the wooden cube be Lcm. In initial case, the wooden cube was floating completely submerged just below the water surface.
When the mass of 200gm is removed, the cube comes out 2cm above the water surface, which means that weight of the mass was balanced by the weight of the liquid displaced corresponding to the volume of the exposed part of cube. Volume of the exposed part of the cube, V=(L2×2)cm3=2L2×10−6m3 Weight of fluid displaced by the exposed part of the cube Wf=V×ρf×g Weight of 200gm mass is, W=mg=200×10−3×10N
Hence we can write, Weight of mass=Weight of fluid displaced Or W=Wf ⇒200×10−3×10=V×ρf×g ∵ρf=1000kg/m3 ⇒200×10−2=2L2×10−6×1000×10 ⇒L2=100 ∴L=10cm is the required side of cube.