Q8. A floating ice cube displaces it own mass "m" of water (i.e. the "hole" it makes below the water surface has the same volume as "m" kg of water). When the ice cube melts it becomes "m" kg of water and exactly fills the hole below the water surface with none left over. The water level will therefore be unchanged.
(a) When the water was placed into the water is displaced its weight of water and the water level rose. When it is removed it drops back to its original level.
(b) When the anchor was first placed into the boat, the boat had to displace an additional volume of water having the same weight as the anchor. The boat sunk deeper below the water surface and the water level rose as this water came out around the boat. When the anchor is removed and placed on the side, this volume of water is no longer displaced. The boat rises in the water and the water level drops.
(c) When the anchor is dropped into the water, it falls to the bottom because its weight is much greater than the weight of the water that it displaces. A volume of water is displaced which is equal to the volume of the anchor and the water level rises. The boat is not higher or lower in the water because the anchor is not touching the boat. When the anchor was placed in the boat, the boat displaced the anchor's weight of water which is greater than the anchor's volume of water. This displacement of more water caused the water level to rise more than when the anchor was dropped into the water.
P5. Another way to do this problem is to notice that 63.44 g of water fills the bottle. Using the density formula you can calculate the volume of 63.44 g of water which is also the internal volume of the bottle. When 53.78 g of fluid was placed into the bottle, the bottle was also completely filled. The density of this fluid must equal the mass of fluid divided by the same volume found for the water. This density divided by the density of water equal the specific gravity of the fluid.
P16. Notice that heights in centimeters were used in this calculation rather than meters. Since every term in the final equation contained a height, the conversion factor changing cm to m is in every term and it cancelled. Knowing when you can "fudge" the units with impunity is a little tricky and it is better to convert everything to consistent SI units when doing calculations.
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