A `0.5 kg` block of brass (density `8xx103Kg m^(-3)`) is suspended from a string. What is the tension in the string if the block is completely immersed in water? `(g =10ms^(-2))`

Options

A. `5N`
B. `(0.5)/(8xx10^(3))N`
C. `5/8 N`
D. `[5-(5)/(8)]N`

Explanation

To find the tension in the string when the brass block is completely immersed in water, we will follow these steps:

### Step 1: Calculate the true weight of the brass block.
The true weight (W) of the block can be calculated using the formula:
\[ W = m \cdot g \]
where:
- \( m = 0.5 \, \text{kg} \) (mass of the block)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values:
\[ W = 0.5 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 5 \, \text{N} \]

### Step 2: Calculate the volume of the brass block.
The volume (V) of the block can be calculated using the formula:
\[ V = \frac{m}{\rho} \]
where:
- \( \rho = 8 \times 10^3 \, \text{kg/m}^3 \) (density of brass)

Substituting the values:
\[ V = \frac{0.5 \, \text{kg}}{8 \times 10^3 \, \text{kg/m}^3} = \frac{0.5}{8000} = 6.25 \times 10^{-5} \, \text{m}^3 \]

### Step 3: Calculate the weight of the water displaced.
The weight of the water displaced (W_displaced) can be calculated using the formula:
\[ W_{\text{displaced}} = V \cdot \rho_{\text{water}} \cdot g \]
where:
- \( \rho_{\text{water}} = 10^3 \, \text{kg/m}^3 \) (density of water)

Substituting the values:
\[ W_{\text{displaced}} = 6.25 \times 10^{-5} \, \text{m}^3 \cdot 10^3 \, \text{kg/m}^3 \cdot 10 \, \text{m/s}^2 \]
\[ W_{\text{displaced}} = 6.25 \times 10^{-5} \cdot 1000 \cdot 10 = 0.625 \, \text{N} \]

### Step 4: Calculate the apparent weight of the block.
The apparent weight (W_apparent) of the block when submerged is given by:
\[ W_{\text{apparent}} = W - W_{\text{displaced}} \]
Substituting the values:
\[ W_{\text{apparent}} = 5 \, \text{N} - 0.625 \, \text{N} = 4.375 \, \text{N} \]

### Step 5: Determine the tension in the string.
The tension (T) in the string is equal to the apparent weight of the block:
\[ T = W_{\text{apparent}} = 4.375 \, \text{N} \]

Thus, the tension in the string when the block is completely immersed in water is **4.375 N**.

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