Assertion: Weight of solid in air is w and in water is `(2w)/(3)`.Then relative density of solid is `3.0`.
Reason: Relative density of any solid is given by
` RD=("Weight in air")/("Change in weight in water")`.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Answer

To solve the problem, we need to analyze the assertion and the reason provided regarding the relative density of a solid.

### Step 1: Understand the Given Information
- The weight of the solid in air is denoted as \( W \).
- The weight of the solid in water is given as \( \frac{2W}{3} \).

### Step 2: Calculate the Change in Weight in Water
The change in weight when the solid is submerged in water can be calculated as follows:
\[ \text{Change in weight in water} = \text{Weight in air} - \text{Weight in water} \]
Substituting the values:
\[ \text{Change in weight in water} = W - \frac{2W}{3} \]
To simplify this, we can express \( W \) as \( \frac{3W}{3} \):
\[ \text{Change in weight in water} = \frac{3W}{3} - \frac{2W}{3} = \frac{W}{3} \]

### Step 3: Calculate the Relative Density
Relative density (RD) is defined as the ratio of the weight in air to the change in weight in water:
\[ RD = \frac{\text{Weight in air}}{\text{Change in weight in water}} \]
Substituting the values we have:
\[ RD = \frac{W}{\frac{W}{3}} = W \times \frac{3}{W} = 3 \]

### Step 4: Conclusion
From our calculations, we find that the relative density of the solid is indeed \( 3.0 \).

### Step 5: Evaluate the Assertion and Reason
- **Assertion**: The weight of the solid in air is \( W \) and in water is \( \frac{2W}{3} \). This is true.
- **Reason**: Relative density of any solid is given by \( RD = \frac{\text{Weight in air}}{\text{Change in weight in water}} \). This is also true.

Since both the assertion and the reason are correct and the reason correctly explains the assertion, we conclude that both are true.

### Final Answer
Both the assertion and reason are true, and the reason correctly explains the assertion.

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