A sample of metal weighs 210 g in air , 180 in water , and 120 in liquid . Then , relative density of

Options

A. metal is 3
B. metal is 7
C. liquid is 3
D. liquid is 1/3

Answer

To find the relative density of the metal sample, we can follow these steps:

### Step 1: Understand the given weights
- Weight of the metal in air (W_air) = 210 g
- Weight of the metal in water (W_water) = 180 g
- Weight of the metal in liquid (W_liquid) = 120 g

### Step 2: Calculate the loss of weight in water
The loss of weight when the metal is submerged in water can be calculated as:
\[ \text{Loss of weight in water} = W_{\text{air}} - W_{\text{water}} = 210 \, \text{g} - 180 \, \text{g} = 30 \, \text{g} \]

### Step 3: Calculate the volume of the metal
The loss of weight in water is equal to the weight of the water displaced, which can be expressed using the formula:
\[ \text{Loss of weight} = \text{Weight of water displaced} = \rho_{\text{water}} \cdot V \]
Where \( \rho_{\text{water}} \) is the density of water (approximately 1 g/cm³). Therefore, we can write:
\[ 30 \, \text{g} = 1 \, \text{g/cm}^3 \cdot V \]
Thus, the volume \( V \) of the metal is:
\[ V = 30 \, \text{cm}^3 \]

### Step 4: Calculate the density of the metal
Now, we can calculate the density of the metal (\( \rho_{\text{metal}} \)):
\[ \rho_{\text{metal}} = \frac{\text{mass}}{\text{volume}} = \frac{210 \, \text{g}}{30 \, \text{cm}^3} = 7 \, \text{g/cm}^3 \]

### Step 5: Calculate the relative density of the metal
Relative density (specific gravity) is the ratio of the density of the substance to the density of water:
\[ \text{Relative Density} = \frac{\rho_{\text{metal}}}{\rho_{\text{water}}} = \frac{7 \, \text{g/cm}^3}{1 \, \text{g/cm}^3} = 7 \]

### Final Answer:
The relative density of the metal is **7**.

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