A body of density `rho` is immersed in a liquid of density `rho_(L)`.State condition when the body will (i) float (ii) sink in liquid.

Answer

To determine the conditions under which a body of density \( \rho \) will float or sink in a liquid of density \( \rho_L \), we can analyze the relationship between the densities of the body and the liquid.

### Step-by-Step Solution:

1. **Understanding the Concept of Density**:
- Density is defined as mass per unit volume. A body will experience buoyancy when placed in a fluid, which is the upward force exerted by the fluid.

2. **Condition for Floating**:
- A body will float in a liquid if its density is less than or equal to the density of the liquid. Mathematically, this condition can be expressed as:
\[ \rho \leq \rho_L \]
- This means:
- If the density of the body \( \rho \) is less than the density of the liquid \( \rho_L \), the body will float.
- If the density of the body \( \rho \) is equal to the density of the liquid \( \rho_L \), the body will also float (it will be neutrally buoyant).

3. **Condition for Sinking**:
- A body will sink in a liquid if its density is greater than the density of the liquid. This condition can be expressed as:
\[ \rho > \rho_L \]
- In this case, the weight of the body is greater than the buoyant force acting on it, causing it to sink.

### Summary of Conditions:
- **Float**: \( \rho \leq \rho_L \)
- **Sink**: \( \rho > \rho_L \)