An iron block is suspended from a string and is then completely immersed in a container of water. The mass of iron is 1 kg and its density is `7200 kg //m^(3) ` . What is the tension in the string before and after the iron block is immersed ?

Explanation

To find the tension in the string before and after the iron block is immersed in water, we will follow these steps:

### Step 1: Calculate the weight of the iron block
The weight \( W \) of the iron block can be calculated using the formula:
\[ W = mg \]
where:
- \( m = 1 \, \text{kg} \) (mass of the iron block)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating:
\[ W = 1 \times 9.8 = 9.8 \, \text{N} \]

### Step 2: Determine the tension in the string before immersion
Before the block is immersed in water, the only forces acting on it are its weight and the tension in the string. Since the block is in equilibrium, the tension \( T_1 \) in the string is equal to the weight of the block:
\[ T_1 = W = 9.8 \, \text{N} \]

### Step 3: Calculate the volume of the iron block
The volume \( V_s \) of the iron block can be calculated using its density \( \rho_s \):
\[ V_s = \frac{m}{\rho_s} \]
where:
- \( \rho_s = 7200 \, \text{kg/m}^3 \)

Calculating:
\[ V_s = \frac{1}{7200} \approx 0.00013889 \, \text{m}^3 \]

### Step 4: Calculate the buoyant force when the block is immersed
The buoyant force \( F_b \) acting on the block when it is fully immersed can be calculated using Archimedes' principle:
\[ F_b = \rho_l V_s g \]
where:
- \( \rho_l = 1000 \, \text{kg/m}^3 \) (density of water)

Calculating:
\[ F_b = 1000 \times 0.00013889 \times 9.8 \approx 1.363 \, \text{N} \]

### Step 5: Determine the tension in the string after immersion
After the block is immersed, the tension \( T_2 \) in the string can be calculated using the equation:
\[ T_2 = W - F_b \]
Substituting the values:
\[ T_2 = 9.8 - 1.363 \approx 8.437 \, \text{N} \]

### Final Results
- Tension before immersion: \( T_1 = 9.8 \, \text{N} \)
- Tension after immersion: \( T_2 \approx 8.44 \, \text{N} \)