If an object sinks in water, it means that

Analysis of the Question

This question tests your understanding of Archimedes' Principle and the Law of Flotation. It asks for the physical condition that causes an object to sink when placed in a fluid (in this case, water).

Concept Explanation

To determine whether an object will float or sink, we compare two forces acting on it:

1. Weight ($W$): The downward force due to gravity ($W = mg$).
2. Upthrust ($U$): The upward force exerted by the fluid on the object.

According to the Law of Flotation:

• If Weight > Upthrust, the object sinks.
• If Weight = Upthrust, the object floats (is in equilibrium).
• If Weight < Upthrust, the object rises to the surface.

Since Weight is related to density ($\rho_{object} \times V \times g$) and Upthrust is related to the density of the fluid ($\rho_{fluid} \times V \times g$), the condition for sinking simplifies to the density of the object being greater than the density of the fluid.

Step-by-Step Solution

1. Define the variables: Let $\rho_o$ be the density of the object and $\rho_w$ be the density of water.
2. Analyze the sinking condition: An object sinks when the gravitational force pulling it down is greater than the buoyant force (upthrust) pushing it up.
3. Relate to density: • Weight of object = $\rho_o \times V \times g$ • Upthrust = $\rho_w \times V \times g$
4. Compare: For the object to sink, $\rho_o \times V \times g > \rho_w \times V \times g$.
5. Conclusion: By canceling out the common terms ($V$ and $g$), we find that $\rho_o > \rho_w$. This means the density of the object must be greater than the density of the water.

Identifying the Answer

• Option A: Correct. If the object is denser than water, it will sink.
• Option B: Incorrect. If upthrust equals weight, the object will float in equilibrium.
• Option C: Incorrect. If the density is less than water, the object will float.
• Option D: Incorrect. Water pressure acts in all directions and is not the primary factor determining sinking; density is.

Exam Tip

Think of it this way: "Denser sinks, lighter floats." If you ever get confused in the exam hall, remember a stone (high density) sinks in water, while a piece of wood (low density) floats. This simple mental model will help you remember the relationship between density and buoyancy every time!