A solid weighs `10 N` in air. Its weight decreases by `2 N` when weighed in water what is the density of solid?

Answer

To find the density of the solid, we can follow these steps:

### Step 1: Understand the given information
- The weight of the solid in air (W_air) = 10 N
- The weight of the solid in water (W_water) = W_air - Loss of weight in water = 10 N - 2 N = 8 N

### Step 2: Calculate the buoyant force
The loss of weight when the solid is submerged in water is equal to the buoyant force acting on it. Therefore, the buoyant force (F_b) is:
\[ F_b = 2 \, \text{N} \]

### Step 3: Use Archimedes' principle
According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the solid. This can be expressed as:
\[ F_b = \text{Volume of solid} \times \text{Density of water} \times g \]
Where:
- Density of water (ρ_water) = 1000 kg/m³ (approximately)
- g = acceleration due to gravity = 9.81 m/s² (approximately)

### Step 4: Calculate the volume of the solid
From the buoyant force equation:
\[ 2 \, \text{N} = V \times 1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2 \]
Where V is the volume of the solid.

Rearranging the equation to find V:
\[ V = \frac{2 \, \text{N}}{1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2} \]
\[ V = \frac{2}{9810} \, \text{m}^3 \]
\[ V \approx 0.000203 \, \text{m}^3 \]

### Step 5: Calculate the density of the solid
The density of the solid (ρ_solid) can be calculated using the formula:
\[ \rho_{\text{solid}} = \frac{\text{Weight in air}}{g \times V} \]
Substituting the values:
\[ \rho_{\text{solid}} = \frac{10 \, \text{N}}{9.81 \, \text{m/s}^2 \times 0.000203 \, \text{m}^3} \]
\[ \rho_{\text{solid}} \approx \frac{10}{0.00199643} \]
\[ \rho_{\text{solid}} \approx 5000 \, \text{kg/m}^3 \]

### Final Answer
The density of the solid is approximately **5000 kg/m³**.

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