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Question

A wooden cube just floats inside water with a 200 gm mass placed on it. When the mass is removed, the cube floats with its top surface 2 cm above the water level. What is the side of the cube? [Take g=10 m/s2]

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 cm
Let the side of the wooden cube be L cm.
In initial case, the wooden cube was floating completely submerged just below the water surface.


When the mass of 200 gm is removed, the cube comes out 2 cm 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=2L2×106 m3
Weight of fluid displaced by the exposed part of the cube
Wf=V×ρf×g
Weight of 200 gm mass is,
W=mg=200×103×10 N

Hence we can write,
Weight of mass=Weight of fluid displaced
Or W=Wf
200×103×10=V×ρf×g
ρf=1000 kg/m3
200×102=2L2×106×1000×10
L2=100
L=10 cm is the required side of cube.

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