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Floating and Sinking

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Question

We have a vessel in shape of a cuboid partially filled with water. Its base is square with an area of $4.5 d m^{2} (1 d m = 10 c m)$ and vessel contains water up to $2 c m$ height. Then we place a wooden cube inside water. The wood has mass of $4 k g$ and specific gravity $0.5$ . The base of wooden cube is horizontal. Find the height of water level above the base of wooden block.

5 c m

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10 c m

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7 c m

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15 c m

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Solution

The correct option is B $10 c m$
Let the side of the cuboid $= a$

Then volume of the cuboid $= a^{3}$

Points $A$ and $B$ are at the same level so, Pressure at $A$ and $B$ will be same

$m = a^{3} p$

$4 = a^{3} \times 500$

$a = 1 / 5 m$

$P_{0} + p g h = P_{0} + \frac{m g}{A}$

$h = 10 c m$

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