1. A completely submerged object always displaces its own:
Verification Matrix:
By definition, when a solid body is fully immersed inside a fluid space, it must occupy a physical spatial region equal to its total dimensions. Therefore, the volume of fluid pushed aside or displaced ($V_{\text{displaced}}$) is precisely equal to the total volume of the submerged object ($V_{\text{object}}$).
2. The pressure exerted on the ground by a man is greatest when:
Verification Matrix:
Pressure is defined by the formula $P = \frac{F}{A}$. The downward force ($F$) matches the man's constant weight ($mg$). To maximize pressure, the contact area ($A$) must be minimized. Standing on the toes of just one foot yields the absolute smallest surface distribution profile, maximizing pressure.
3. In a stationary homogeneous liquid:
Verification Matrix:
Hydrostatic pressure inside a continuous, stationary fluid depends purely on depth ($h$) below the surface, governed by $P = P_0 + \rho gh$. Points along the same horizontal line or level share an identical depth parameter ($h$), meaning they experience identical pressure fields.
4. One piston in a hydraulic lift has an area that is twice the area of the other. When the pressure at the smaller piston is increased by $\Delta p$, the pressure at the larger piston:
Verification Matrix:
According to **Pascal's Principle**, any change in pressure applied to an enclosed, incompressible fluid is transmitted undiminished to every single portion of the fluid and the walls of its container. Thus, the pressure increment is exactly identical ($\Delta p$) at both pistons, regardless of area.
5. In a vacuum, an object has:
Verification Matrix:
Buoyant force is created by surrounding fluid displacement and is modeled by $F_b = \rho_{\text{fluid}} V g$. Because a vacuum represents a space entirely devoid of matter ($\rho_{\text{fluid}} = 0$), no fluid medium exists to be displaced, eliminating any upward buoyant vector entirely.
6. The pressure at the bottom of a pond does NOT depend on:
Verification Matrix:
The hydrostatic formula $P = \rho g h$ shows that local fluid pressure depends exclusively on fluid density ($\rho$), acceleration due to gravity ($g$), and vertical depth ($h$). The structural width or surface cross-sectional area ($A$) of the body of water does not affect pressure.
7. A rock suspended by a weighing scale weighs $5\text{ N}$ out of water and $3\text{ N}$ when submerged in water. What is the buoyant force on the rock?
Verification Matrix:
Apparent weight within a fluid medium equals the true atmospheric weight minus the supporting upward buoyant force vector: $W_{\text{apparent}} = W_{\text{actual}} - F_b$. Rearranging this expression yields: $F_b = W_{\text{actual}} - W_{\text{apparent}} = 5\text{ N} - 3\text{ N} = 2\text{ N}$.
8. "An object completely submerged in a fluid displaces its own volume of fluid". This is:
Verification Matrix:
While **Archimedes' Principle** links buoyant force to the *weight* of the displaced fluid ($F_b = m_{\text{fluid}}g$), the fact that a fully submerged object shifts a *volume* equal to its own is a geometric consequence of matter impenetrability. Because none of the named laws specifically state this volume rule as their core principle, option (d) is the correct choice.
9. Salt water has greater density than freshwater. A boat floats in both freshwater and saltwater. The buoyant force on the boat in salt water is ________ that in freshwater.
Verification Matrix:
For any stably floating object, the upward buoyant force must precisely balance the object's downward weight ($F_b = W_{\text{boat}}$) to maintain vertical equilibrium ($\Sigma F_y = 0$). Because the boat's total weight remains unchanged between both environments, the buoyant forces must be equal. (Note: The boat simply sits higher in saltwater, displacing less volume). Options (a) and (d) are conceptually identical, making (a) the standard selection.
10. You fill a tall glass with ice and then add water to the level of the glass's rim, so some fraction of the ice floats above the rim. When the ice melts, what happens to the water level?
Verification Matrix:
A floating ice cube displaces a volume of liquid water whose weight matches the total weight of the ice cube. When that ice melts, it transitions into liquid water while conserving its mass and weight. The melted water occupies the exact submerged volume the ice cube originally displaced, keeping the water level perfectly at the rim.
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