A wooden block of volume `1000cm^(3)` is suspended from a spring balance its weight is 12 N in air. It is suspended in water such that half of the block is below the surface of water. The reading of spring balance is

Options

A. 10 N
B. 9N
C. 8 N
D. 7 N

Answer

To solve the problem step by step, we will analyze the forces acting on the wooden block when it is submerged in water.

### Step 1: Understand the given data
- Volume of the wooden block, \( V = 1000 \, \text{cm}^3 \)
- Weight of the block in air, \( W = 12 \, \text{N} \)
- Half of the block is submerged in water.

### Step 2: Calculate the weight of the block
The weight of the block is already given as \( W = 12 \, \text{N} \).

### Step 3: Calculate the buoyant force
The buoyant force (\( F_b \)) can be calculated using Archimedes' principle. The buoyant force is equal to the weight of the fluid displaced by the submerged part of the block.

Since half of the block is submerged:
- Volume of the submerged part, \( V_{sub} = \frac{V}{2} = \frac{1000 \, \text{cm}^3}{2} = 500 \, \text{cm}^3 \)

To calculate the buoyant force:
1. Convert the volume from cm³ to m³:
\[ V_{sub} = 500 \, \text{cm}^3 = 500 \times 10^{-6} \, \text{m}^3 = 5 \times 10^{-4} \, \text{m}^3 \]
2. Use the density of water (\( \rho \)) which is approximately \( 1000 \, \text{kg/m}^3 \).
3. Use \( g = 10 \, \text{m/s}^2 \).

Now calculate the buoyant force:
\[ F_b = V_{sub} \times \rho \times g = 5 \times 10^{-4} \, \text{m}^3 \times 1000 \, \text{kg/m}^3 \times 10 \, \text{m/s}^2 = 5 \, \text{N} \]

### Step 4: Apply the equilibrium condition
When the block is submerged, the forces acting on it are:
- Downward force (weight of the block, \( W = 12 \, \text{N} \))
- Upward force (buoyant force, \( F_b = 5 \, \text{N} \))
- Tension in the spring balance (\( T \))

According to the equilibrium condition:
\[ T + F_b = W \]
Rearranging gives:
\[ T = W - F_b \]

### Step 5: Substitute the values
Substituting the values we have:
\[ T = 12 \, \text{N} - 5 \, \text{N} = 7 \, \text{N} \]

### Conclusion
The reading of the spring balance when the block is submerged in water is \( 7 \, \text{N} \).

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