If a block of iron (density `5g cm^(-3))` is size 5 cm xx 5 cm xx 5 cm was weight while completely submerged in water, what would be the apperent weight ?

Options

A. 5xx5xx5xx5 gf
B. 4xx4xx4xx5 gf
C. 3xx5xx5xx5 gf
D. 4xx5xx5xx5 gf

Explanation

To find the apparent weight of the block of iron when submerged in water, we can follow these steps:

### Step 1: Calculate the Volume of the Iron Block
The volume \( V \) of the iron block can be calculated using the formula for the volume of a cube:
\[ V = \text{side}^3 \]
Given that the side length is 5 cm:
\[ V = 5 \, \text{cm} \times 5 \, \text{cm} \times 5 \, \text{cm} = 125 \, \text{cm}^3 \]

### Step 2: Calculate the True Weight of the Iron Block
The true weight \( W \) of the iron block can be calculated using the formula:
\[ W = V \times \text{density} \times g \]
Given that the density of iron is \( 5 \, \text{g/cm}^3 \) and taking \( g \) (acceleration due to gravity) as \( 9.8 \, \text{m/s}^2 \) (or \( 980 \, \text{cm/s}^2 \) for consistency in units):
\[ W = 125 \, \text{cm}^3 \times 5 \, \text{g/cm}^3 \times 980 \, \text{cm/s}^2 \]
\[ W = 125 \times 5 \times 980 = 612500 \, \text{g cm/s}^2 = 612.5 \, \text{N} \]

### Step 3: Calculate the Weight of Water Displaced
The weight of the water displaced can be calculated using the same volume but using the density of water:
\[ W_{\text{water}} = V \times \text{density}_{\text{water}} \times g \]
The density of water is \( 1 \, \text{g/cm}^3 \):
\[ W_{\text{water}} = 125 \, \text{cm}^3 \times 1 \, \text{g/cm}^3 \times 980 \, \text{cm/s}^2 \]
\[ W_{\text{water}} = 125 \times 1 \times 980 = 122500 \, \text{g cm/s}^2 = 122.5 \, \text{N} \]

### Step 4: Calculate the Apparent Weight
The apparent weight \( W_{\text{apparent}} \) can be calculated using the formula:
\[ W_{\text{apparent}} = W - W_{\text{water}} \]
Substituting the values we calculated:
\[ W_{\text{apparent}} = 612.5 \, \text{N} - 122.5 \, \text{N} = 490 \, \text{N} \]

### Conclusion
The apparent weight of the block of iron when submerged in water is \( 490 \, \text{N} \).

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