A body of mass 3.5 kg displaces `1000cm^(3)` of water when fully immersed inside it. Calculate :(i) the volume of body (ii) the upthrust on body and (iii) the apparent weight of body in water.

Answer

Let's solve the problem step by step.

### Given:
- Mass of the body, \( m = 3.5 \, \text{kg} \)
- Volume of water displaced, \( V_{\text{displaced}} = 1000 \, \text{cm}^3 \)

### Step 1: Calculate the Volume of the Body
According to Archimedes' principle, the volume of the body is equal to the volume of water displaced when the body is fully immersed.

\[ V_{\text{body}} = V_{\text{displaced}} = 1000 \, \text{cm}^3 \]

To convert this volume into cubic meters:

\[ 1000 \, \text{cm}^3 = 1000 \times 10^{-6} \, \text{m}^3 = 10^{-3} \, \text{m}^3 \]

So, the volume of the body is:

\[ V_{\text{body}} = 10^{-3} \, \text{m}^3 \]

### Step 2: Calculate the Upthrust on the Body
The upthrust (or buoyant force) acting on the body can be calculated using the formula:

\[ \text{Upthrust} = V \cdot \rho \cdot g \]

Where:
- \( V \) is the volume of the body (or water displaced) = \( 10^{-3} \, \text{m}^3 \)
- \( \rho \) is the density of water = \( 1000 \, \text{kg/m}^3 \)
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \))

Substituting the values:

\[ \text{Upthrust} = 10^{-3} \, \text{m}^3 \times 1000 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2 \]

Calculating:

\[ \text{Upthrust} = 10^{-3} \times 1000 \times 9.8 = 9.8 \, \text{N} \]

### Step 3: Calculate the Apparent Weight of the Body in Water
The apparent weight of the body in water can be calculated using the formula:

\[ \text{Apparent Weight} = \text{True Weight} - \text{Upthrust} \]

Where:
- True Weight = \( m \cdot g = 3.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 34.3 \, \text{N} \)
- Upthrust = \( 9.8 \, \text{N} \)

Substituting the values:

\[ \text{Apparent Weight} = 34.3 \, \text{N} - 9.8 \, \text{N} = 24.5 \, \text{N} \]

### Summary of Results
1. Volume of the body: \( 10^{-3} \, \text{m}^3 \)
2. Upthrust on the body: \( 9.8 \, \text{N} \)
3. Apparent weight of the body in water: \( 24.5 \, \text{N} \)

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