An ornament weighing `50g` in air weighs only `46 g` in water. Assuming that some copper is mixed with gold to prepare the ornament, find the amount of copper in it. Specific gravity of gold is `20` and that of copper is `10`.

Options

A. `20 g`
B. `10 g`
C. `30 g`
D. `40 g`

Explanation

To solve the problem, we need to find the amount of copper mixed with gold in the ornament. We will use the principles of buoyancy and specific gravity to derive the solution step by step.

### Step-by-Step Solution:

1. **Understand the Problem**:
- The ornament weighs 50 g in air and 46 g in water.
- The loss of weight in water is due to the buoyant force acting on it.

2. **Calculate the Loss of Weight**:
- Loss of weight in water = Weight in air - Weight in water
- Loss of weight = 50 g - 46 g = 4 g

3. **Relate Loss of Weight to Buoyant Force**:
- According to Archimedes' principle, the loss of weight is equal to the buoyant force.
- Buoyant force = Volume of displaced water × Density of water × g
- Here, the density of water is 1 g/cm³ (since specific gravity of water is 1).

4. **Calculate the Volume of the Ornament**:
- Since the loss of weight is 4 g, this means the volume of the ornament (V) can be calculated as:
- Volume (V) = Loss of weight / Density of water = 4 g / 1 g/cm³ = 4 cm³

5. **Set Up the Masses**:
- Let the mass of copper in the ornament be M grams.
- Therefore, the mass of gold in the ornament will be (50 - M) grams.

6. **Calculate the Volumes of Gold and Copper**:
- The volume of copper (V_copper) = Mass of copper / Density of copper = M / 10 cm³ (since specific gravity of copper is 10).
- The volume of gold (V_gold) = Mass of gold / Density of gold = (50 - M) / 20 cm³ (since specific gravity of gold is 20).

7. **Total Volume of the Ornament**:
- The total volume of the ornament is the sum of the volumes of gold and copper:
- V = V_copper + V_gold
- Therefore, we have:
- 4 cm³ = (M / 10) + ((50 - M) / 20)

8. **Solve the Equation**:
- Multiply the entire equation by 20 to eliminate the denominators:
- 80 = 2M + (50 - M)
- Simplifying gives:
- 80 = 2M + 50 - M
- 80 = M + 50
- M = 80 - 50
- M = 30 grams

9. **Conclusion**:
- The mass of copper in the ornament is 30 grams.
- The mass of gold in the ornament is 50 - 30 = 20 grams.

### Final Answer:
- The amount of copper in the ornament is **30 grams**.