A block of silver of mass `4 kg` hanging from a string is immersed in a liquid of relative density `0.72`. If relative density of silver is `10`, then tension in the string will be

Options

A. `37.12N`
B. `42N`
C. `73N`
D. `21N`

Explanation

To find the tension in the string holding the block of silver immersed in a liquid, we can follow these steps:

### Step 1: Identify the forces acting on the block
The forces acting on the block are:
- The weight of the block (W) acting downwards.
- The buoyant force (B) acting upwards.
- The tension in the string (T) acting upwards.

### Step 2: Write the equation of motion
According to the equilibrium of forces, we can write:
\[ T + B = W \]
Where:
- \( W = mg \) (weight of the block)
- \( B = \text{Buoyant force} \)

Rearranging gives:
\[ T = W - B \]

### Step 3: Calculate the weight of the block
Given:
- Mass of the silver block \( m = 4 \, \text{kg} \)
- Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \)

The weight \( W \) is:
\[ W = mg = 4 \, \text{kg} \times 10 \, \text{m/s}^2 = 40 \, \text{N} \]

### Step 4: Calculate the buoyant force
The buoyant force \( B \) can be calculated using the formula:
\[ B = \text{Volume of liquid displaced} \times \text{Density of liquid} \times g \]

First, we need to find the volume of the silver block. The volume \( V \) can be calculated using the relative density:
- Relative density of silver = 10
- Density of silver \( \rho_s = 10 \times 1000 \, \text{kg/m}^3 = 10000 \, \text{kg/m}^3 \)

Thus, the volume \( V \) of the silver block is:
\[ V = \frac{m}{\rho_s} = \frac{4 \, \text{kg}}{10000 \, \text{kg/m}^3} = 0.0004 \, \text{m}^3 \]

Now, we can find the buoyant force. The relative density of the liquid is given as 0.72, which means:
- Density of liquid \( \rho_l = 0.72 \times 1000 \, \text{kg/m}^3 = 720 \, \text{kg/m}^3 \)

Now we can calculate the buoyant force \( B \):
\[ B = V \times \rho_l \times g = 0.0004 \, \text{m}^3 \times 720 \, \text{kg/m}^3 \times 10 \, \text{m/s}^2 \]
\[ B = 0.0004 \times 7200 = 2.88 \, \text{N} \]

### Step 5: Calculate the tension in the string
Now substituting the values of \( W \) and \( B \) into the tension equation:
\[ T = W - B = 40 \, \text{N} - 2.88 \, \text{N} = 37.12 \, \text{N} \]

### Final Answer
The tension in the string is \( 37.12 \, \text{N} \).

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