A box contains some identical red coloured balls labelled as A, each weighing 2g. Another box contains identical blue coloured balls, labelled as B, each weighing 5 g. In the combinations AB,`AB_2, A_2B` and `A_2B_3` which law is applicable ?

Options

A. Law of definite proportion
B. Law of multiple proportion
C. Law of conservation of mass
D. None of the above

Answer

To determine which law is applicable to the combinations of balls A and B, we need to analyze the mass ratios of the elements involved in the different combinations. Let's break down the steps:

### Step 1: Identify the Masses
- Each red ball (A) weighs 2 g.
- Each blue ball (B) weighs 5 g.

### Step 2: Calculate the Masses for Each Combination
1. **For AB**:
- Mass of A = 2 g
- Mass of B = 5 g
- Total mass = 2 g + 5 g = 7 g

2. **For AB₂**:
- Mass of A = 2 g
- Mass of 2 B = 2 × 5 g = 10 g
- Total mass = 2 g + 10 g = 12 g

3. **For A₂B**:
- Mass of 2 A = 2 × 2 g = 4 g
- Mass of B = 5 g
- Total mass = 4 g + 5 g = 9 g

4. **For A₂B₃**:
- Mass of 2 A = 2 × 2 g = 4 g
- Mass of 3 B = 3 × 5 g = 15 g
- Total mass = 4 g + 15 g = 19 g

### Step 3: Analyze the Ratios
Now we will analyze the ratios of the masses of B in each combination while keeping the mass of A constant.

1. For **AB**:
- Mass of B = 5 g when A = 2 g.

2. For **AB₂**:
- Mass of B = 10 g when A = 2 g.

3. For **A₂B**:
- Mass of B = 5 g when A = 4 g (which is equivalent to 2 g of A in the ratio).

4. For **A₂B₃**:
- Mass of B = 15 g when A = 4 g (which is equivalent to 2 g of A in the ratio).

### Step 4: Establish the Whole Number Ratios
Now we will express the mass of B in terms of a fixed mass of A (let's take 2 g of A as the reference):

- For AB: B = 5 g
- For AB₂: B = 10 g
- For A₂B: B = 5 g
- For A₂B₃: B = 15 g

Now, we can express these in terms of a fixed mass of A (2 g):

- For AB: 5 g of B
- For AB₂: 10 g of B
- For A₂B: 5 g of B
- For A₂B₃: 15 g of B

### Step 5: Calculate the Ratios
Now we can find the ratios of the masses of B for the different combinations:

- For AB: 5 g
- For AB₂: 10 g
- For A₂B: 5 g
- For A₂B₃: 15 g

If we take the ratios of B to A (keeping A constant), we get:

- AB: 5/2
- AB₂: 10/2
- A₂B: 5/4
- A₂B₃: 15/4

### Conclusion
The ratios of the masses of B (when A is fixed) are in whole numbers (2:4:1:3). This demonstrates that the law of multiple proportions is applicable here.