A piece of wax wieghs 18.03 g in air. A piece of metal is found to weigh 17.03 g in water. It is tied to the wax and both together weigh 15.23 g in water. Then, the specific gravity of wax is

Options

A. `18.03/17.03`
B. `17.03/18.03`
C. `18.03/19.83`
D. `15.03/19.83`

Answer

To solve the problem, we need to find the specific gravity of the wax using the given weights. The specific gravity (SG) is defined as the ratio of the weight of a substance to the weight of an equal volume of water.

### Step-by-Step Solution:

1. **Identify the Given Weights:**
- Weight of wax in air (W_wax_air) = 18.03 g
- Weight of metal in water (W_metal_water) = 17.03 g
- Weight of wax and metal together in water (W_combined_water) = 15.23 g

2. **Calculate the Weight of Wax in Water (W_wax_water):**
- The weight of the metal in air can be calculated using the buoyant force. The buoyant force is equal to the weight of the water displaced by the metal.
- The weight of the metal in air (W_metal_air) can be calculated as:
\[ W_metal_air = W_metal_water + \text{Buoyant Force} \]
- The buoyant force can be expressed as the difference between the weight of the wax and metal in air and their combined weight in water:
\[ \text{Buoyant Force} = W_metal_air - W_combined_water \]

3. **Calculate the Buoyant Force:**
- First, we need to find the weight of the metal in air:
\[ W_metal_air = W_metal_water + \text{Buoyant Force} \]
- Rearranging gives:
\[ \text{Buoyant Force} = W_metal_air - W_combined_water \]
- The weight of the wax in water can be calculated as:
\[ W_wax_water = W_wax_air - \text{Buoyant Force} \]

4. **Calculate the Specific Gravity of Wax:**
- The specific gravity (SG) of wax is given by the formula:
\[ SG = \frac{W_wax_air}{W_wax_air - W_wax_water} \]
- Substitute the values we have calculated into this formula to find the specific gravity of wax.

### Final Calculation:
1. Calculate the buoyant force:
\[ \text{Buoyant Force} = W_wax_air + W_metal_air - W_combined_water \]
- We need to find \(W_metal_air\) first, which can be derived from the information given.

2. Once we have \(W_wax_water\), we can substitute back into the specific gravity formula to find the final answer.