A block of wood is floating on water with its dimensions `50 cmxx 50 cm xx50cm` inside water. Calculate the buoyant force acting on the block. Take `g=9.8Nkg^(-1)`

Answer

To solve the problem of calculating the buoyant force acting on a block of wood floating on water, we can follow these steps:

### Step 1: Calculate the Volume of the Block
The dimensions of the block are given as 50 cm x 50 cm x 50 cm. First, we need to convert these dimensions into meters for consistency in SI units.

\[ \text{Dimensions in meters} = 0.50 \, \text{m} \times 0.50 \, \text{m} \times 0.50 \, \text{m} \]

Now, calculate the volume:

\[ \text{Volume} = 0.50 \times 0.50 \times 0.50 = 0.125 \, \text{m}^3 \]

### Step 2: Use the Density of Water
The density of water is given as \(1000 \, \text{kg/m}^3\).

### Step 3: Calculate the Mass of the Water Displaced
Using the formula for mass:

\[ \text{Mass} = \text{Density} \times \text{Volume} \]

Substituting the values:

\[ \text{Mass} = 1000 \, \text{kg/m}^3 \times 0.125 \, \text{m}^3 = 125 \, \text{kg} \]

### Step 4: Calculate the Weight of the Water Displaced
The weight of the water displaced can be calculated using the formula:

\[ \text{Weight} (W) = \text{Mass} \times g \]

Where \(g = 9.8 \, \text{N/kg}\):

\[ W = 125 \, \text{kg} \times 9.8 \, \text{N/kg} = 1225 \, \text{N} \]

### Step 5: Determine the Buoyant Force
According to Archimedes' principle, the buoyant force (\(F_b\)) is equal to the weight of the liquid displaced:

\[ F_b = W = 1225 \, \text{N} \]

Thus, the buoyant force acting on the block is **1225 N**.

### Summary of the Solution
The buoyant force acting on the block of wood floating on water is **1225 N**.

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