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A container holds water whose centre of mass is at C, on the vertical line OC. A small wooden piece is then placed floating on the water toward the right side, as shown. After placing the wooden piece, which statement is correct?
- Pressure at base remains same and centre of mass of water and wooden piece will be right of line OC.
- Pressure at base remains same and centre of mass of water and wooden piece will be on line OC.
- Pressure at base changes and centre of mass of water and wooden piece will be right of line OC.
- Pressure at base changes and centre of mass of water and wooden piece will be on line OC.
Correct answer: Pressure at base remains same and centre of mass of water and wooden piece will be right of line OC.
Solution
A floating wooden piece displaces a volume of water equal to its own weight, so the water surface rises uniformly and the pressure at the base (which depends on the height of the liquid column) is the same everywhere as for an equivalent added water mass; the gauge pressure at the base stays effectively the same as it would for the raised uniform level. However, the wooden piece is positioned to the right, so the combined centre of mass of (water + wood) shifts to the right of line OC. Hence option (A).
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