Which one of the following statements is true?

Options

A. The weight of a substance in air is always less than its weight in water.
B. The mass of a substance is equal to the mass of an equal volume of water.
C. The weight of a substance in water is always greater than its weight in some other liquid.
D. The weight of a substance in water is aJways less dun its weight in air.

Answer

To solve the question regarding the comparison of the weight of a substance in air and in water, we can follow these steps:

### Step 1: Understand the Weight of an Object
The weight of an object in air is given by the formula:
\[ W_{\text{air}} = mg \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity.

### Step 2: Understand the Weight of an Object in Water
When an object is submerged in water, it experiences a buoyant force. The weight of the object in water can be expressed as:
\[ W_{\text{water}} = mg - F_b \]
where \( F_b \) is the buoyant force.

### Step 3: Calculate the Buoyant Force
The buoyant force can be calculated using Archimedes' principle:
\[ F_b = \rho V g \]
where:
- \( \rho \) is the density of the fluid (water in this case),
- \( V \) is the volume of the object submerged,
- \( g \) is the acceleration due to gravity.

### Step 4: Substitute the Buoyant Force into the Weight in Water
Now, substituting the expression for buoyant force into the weight in water:
\[ W_{\text{water}} = mg - \rho V g \]

### Step 5: Compare the Two Weights
From the above equations, we can see that:
\[ W_{\text{water}} = mg - \rho V g \]
This shows that the weight of the object in water is less than its weight in air because we are subtracting the buoyant force from the weight in air.

### Conclusion
Thus, we can conclude that:
\[ W_{\text{water}} < W_{\text{air}} \]
This means the weight of the substance in water is always less than its weight in air.

### Final Answer
The correct statement is: "The weight of a substance in water is less than its weight in air."

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