A block weight 15 N in air and 12 N when immersed in water find the specific gravity gravity of block.

Answer

To find the specific gravity of the block, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the weights of the block**:
- Weight of the block in air (W_air) = 15 N
- Weight of the block when immersed in water (W_water) = 12 N

2. **Calculate the buoyant force**:
- The buoyant force (B) acting on the block when it is immersed in water can be calculated as:
\[ B = W_{\text{air}} - W_{\text{water}} = 15 \, \text{N} - 12 \, \text{N} = 3 \, \text{N} \]

3. **Determine the volume of the block**:
- The buoyant force is equal to the weight of the water displaced by the block. Since the density of water is approximately \(1000 \, \text{kg/m}^3\), we can use the formula:
\[ B = \rho_{\text{water}} \cdot g \cdot V \]
where \(V\) is the volume of the block, \(\rho_{\text{water}} = 1000 \, \text{kg/m}^3\), and \(g \approx 9.81 \, \text{m/s}^2\).
- Rearranging gives:
\[ V = \frac{B}{\rho_{\text{water}} \cdot g} = \frac{3 \, \text{N}}{1000 \, \text{kg/m}^3 \cdot 9.81 \, \text{m/s}^2} \]

4. **Calculate the mass of the block**:
- The mass of the block can be calculated using its weight in air:
\[ m = \frac{W_{\text{air}}}{g} = \frac{15 \, \text{N}}{9.81 \, \text{m/s}^2} \approx 1.53 \, \text{kg} \]

5. **Calculate the specific gravity**:
- Specific gravity (SG) is defined as the ratio of the density of the block to the density of water:
\[ SG = \frac{\text{Density of the block}}{\text{Density of water}} = \frac{m/V}{\rho_{\text{water}}} \]
- Since we already know the buoyant force, we can simplify this to:
\[ SG = \frac{W_{\text{air}}}{W_{\text{air}} - W_{\text{water}}} = \frac{15 \, \text{N}}{15 \, \text{N} - 12 \, \text{N}} = \frac{15}{3} = 5 \]

### Final Answer:
The specific gravity of the block is **5**.

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