A block of wood of mass 24 kg floats on water. The volume of wood is `0.032 m^(3)` Find
a.the volume of block below the surface of water,
b.the density of wood.
(Denstiy of water `=1000kgm^(-3)`)

Answer

To solve the problem step by step, we need to find two things:

a. The volume of the block below the surface of water (V1).
b. The density of the wood (ρ).

### Step 1: Understanding the equilibrium condition
When the block of wood floats on water, the buoyant force (Fb) acting on it is equal to the weight of the block (mg).

### Step 2: Write the equation for buoyant force
The buoyant force can be expressed as:
\[ F_b = \rho_w \cdot g \cdot V_d \]
where:
- \( \rho_w \) is the density of water (1000 kg/m³),
- \( g \) is the acceleration due to gravity (which will cancel out),
- \( V_d \) is the volume of water displaced, which is equal to the volume of the block submerged (V1).

### Step 3: Set up the equation for floating condition
Since the block is floating, we can equate the buoyant force to the weight of the block:
\[ F_b = mg \]
Thus, we have:
\[ \rho_w \cdot g \cdot V_1 = mg \]

### Step 4: Rearranging the equation
We can rearrange the equation to find \( V_1 \):
\[ V_1 = \frac{m}{\rho_w} \]

### Step 5: Substitute the known values
Substituting the values we have:
- Mass of the wood (m) = 24 kg
- Density of water (\( \rho_w \)) = 1000 kg/m³

So:
\[ V_1 = \frac{24 \text{ kg}}{1000 \text{ kg/m}^3} \]

### Step 6: Calculate \( V_1 \)
Calculating \( V_1 \):
\[ V_1 = 0.024 \text{ m}^3 \]

### Step 7: Finding the density of wood
Now, we need to find the density of the wood (ρ). The density is given by the formula:
\[ \rho = \frac{m}{V} \]
where:
- \( V \) is the total volume of the wood, which is given as 0.032 m³.

### Step 8: Substitute the known values
Substituting the values we have:
\[ \rho = \frac{24 \text{ kg}}{0.032 \text{ m}^3} \]

### Step 9: Calculate the density of wood
Calculating \( \rho \):
\[ \rho = 750 \text{ kg/m}^3 \]

### Final Answers:
a. The volume of the block below the surface of water (V1) is **0.024 m³**.
b. The density of wood (ρ) is **750 kg/m³**.

---