The R.D of a metal block is `2.7xx10^(3) kg//m^(3)`. It is immersed in water. Then the block

Options

A. sinks
B. flots
C. is partially immersed
D. has no part immersed

Answer

To determine whether the metal block will sink or float in water based on its relative density (R.D.), we can follow these steps:

### Step 1: Understand Relative Density
Relative density (R.D.) is defined as the ratio of the density of a substance to the density of a reference substance (usually water for solids and liquids). The formula is given by:
\[ \text{R.D.} = \frac{\text{Density of the substance}}{\text{Density of water}} \]

### Step 2: Given Data
The relative density of the metal block is given as:
\[ \text{R.D.} = 2.7 \times 10^3 \, \text{kg/m}^3 \]
The density of water is approximately:
\[ \text{Density of water} = 1000 \, \text{kg/m}^3 \]

### Step 3: Calculate the Density of the Metal Block
Using the formula for relative density, we can find the density of the metal block:
\[ \text{Density of the metal block} = \text{R.D.} \times \text{Density of water} \]
Substituting the values:
\[ \text{Density of the metal block} = 2.7 \times 10^3 \, \text{kg/m}^3 \times 1000 \, \text{kg/m}^3 = 2.7 \times 10^6 \, \text{kg/m}^3 \]

### Step 4: Compare Densities
To determine if the block will sink or float, we compare the density of the metal block with the density of water:
- If the density of the block is greater than the density of water, the block will sink.
- If the density of the block is equal to the density of water, the block will float fully submerged.
- If the density of the block is less than the density of water, the block will float partially submerged.

### Step 5: Conclusion
Since the density of the metal block (2.7 x 10^6 kg/m³) is significantly greater than the density of water (1000 kg/m³), we conclude that:
\[ \text{Density of the metal block} > \text{Density of water} \]
Thus, the metal block will **sink** in water.

### Final Answer
The metal block will sink in water.

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