A body weighs 450 gf in air and 310 gf when completely immersed in water. Find:
(i) the volume of the body
(ii) the loss in weight of the body, and
(iii) the upthrust on the body. State the assumption made in part (i)

Answer

To solve the problem step by step, we will follow the instructions given in the question.

### Given:
- Weight of the body in air (W_air) = 450 gf
- Weight of the body in water (W_water) = 310 gf

### (i) Finding the Volume of the Body

1. **Calculate the Loss of Weight**:
The loss of weight when the body is immersed in water can be calculated as:
\[ \text{Loss of Weight} = W_{\text{air}} - W_{\text{water}} = 450 \, \text{gf} - 310 \, \text{gf} = 140 \, \text{gf} \]

2. **Use Archimedes' Principle**:
According to Archimedes' principle, the loss of weight of the body is equal to the upthrust (buoyant force) acting on it, which is also equal to the weight of the fluid displaced by the body.

3. **Calculate the Volume of the Body**:
The volume of the body can be calculated using the formula:
\[ \text{Volume} = \frac{\text{Loss of Weight}}{\text{Density of Water}} \]
The density of water is approximately \(1 \, \text{g/cm}^3\). Therefore,
\[ \text{Volume} = \frac{140 \, \text{gf}}{1 \, \text{g/cm}^3} = 140 \, \text{cm}^3 \]

### (ii) Finding the Loss in Weight of the Body

1. **Calculate the Loss in Weight**:
The loss in weight of the body when immersed in water is already calculated in the first part:
\[ \text{Loss in Weight} = W_{\text{air}} - W_{\text{water}} = 450 \, \text{gf} - 310 \, \text{gf} = 140 \, \text{gf} \]

### (iii) Finding the Upthrust on the Body

1. **Calculate the Upthrust**:
The upthrust (buoyant force) is equal to the loss of weight of the body when immersed in water. Therefore,
\[ \text{Upthrust} = \text{Loss in Weight} = 140 \, \text{gf} \]

### Assumption Made in Part (i)

- The assumption made in part (i) is that the density of water is uniform and equal to \(1 \, \text{g/cm}^3\).

### Summary of Answers:
1. Volume of the body = 140 cm³
2. Loss in weight of the body = 140 gf
3. Upthrust on the body = 140 gf
4. Assumption: The density of water is uniform and equal to \(1 \, \text{g/cm}^3\).

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