A wooden block of mass 8 kg is tied to a string attached to the bottome of the tank. In the equilibrium the block is completely immersed in water. If relative density of wood is 0.8 and `g=10 ms^(-2)`, the tension T, in the string is

Options

A. 120 N
B. 100 N
C. 80 N
D. 20 N

Explanation

To solve the problem, we need to find the tension \( T \) in the string holding a wooden block submerged in water. Here’s a step-by-step solution:

### Step 1: Identify the forces acting on the block
In equilibrium, the forces acting on the block are:
- The **buoyant force** \( F_b \) acting upwards.
- The **weight** of the block \( W \) acting downwards.
- The **tension** \( T \) in the string acting downwards.

### Step 2: Write the equilibrium condition
Since the block is in equilibrium, the sum of the upward forces must equal the sum of the downward forces:
\[ F_b = W + T \]

### Step 3: Calculate the weight of the block
The weight \( W \) of the block can be calculated using the formula:
\[ W = m \cdot g \]
where \( m = 8 \, \text{kg} \) (mass of the block) and \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity).
\[ W = 8 \, \text{kg} \times 10 \, \text{m/s}^2 = 80 \, \text{N} \]

### Step 4: Calculate the volume of the block
The relative density (specific gravity) of the wood is given as \( 0.8 \). This means the density of the wood \( \rho_b \) can be calculated as:
\[ \rho_b = \text{relative density} \times \text{density of water} = 0.8 \times 1000 \, \text{kg/m}^3 = 800 \, \text{kg/m}^3 \]
Now, using the formula for density:
\[ \rho_b = \frac{m}{V} \implies V = \frac{m}{\rho_b} \]
Substituting the values:
\[ V = \frac{8 \, \text{kg}}{800 \, \text{kg/m}^3} = 0.01 \, \text{m}^3 \]

### Step 5: Calculate the buoyant force
The buoyant force \( F_b \) can be calculated using Archimedes' principle:
\[ F_b = \rho_l \cdot V \cdot g \]
where \( \rho_l = 1000 \, \text{kg/m}^3 \) (density of water).
\[ F_b = 1000 \, \text{kg/m}^3 \times 0.01 \, \text{m}^3 \times 10 \, \text{m/s}^2 = 100 \, \text{N} \]

### Step 6: Substitute values into the equilibrium equation
Now substituting \( F_b \) and \( W \) into the equilibrium equation:
\[ 100 \, \text{N} = 80 \, \text{N} + T \]

### Step 7: Solve for tension \( T \)
Rearranging the equation to solve for \( T \):
\[ T = 100 \, \text{N} - 80 \, \text{N} = 20 \, \text{N} \]

### Final Answer
The tension \( T \) in the string is \( 20 \, \text{N} \).

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