A solid weighs 1.5 kgf in air and 0.9 kgf in a liquid of density `1.2xx10^(3)kgm^(-3)`. Calculate R.D. of solid.

Answer

To solve the problem of finding the relative density (R.D.) of a solid given its weight in air and in a liquid, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Weight of the solid in air (WA) = 1.5 kgf
- Weight of the solid in liquid (WL) = 0.9 kgf
- Density of the liquid (ρ_liquid) = 1.2 × 10^3 kg/m³

2. **Calculate the Upthrust (Buoyant Force):**
- Upthrust (U) = Weight in air - Weight in liquid
- U = WA - WL
- U = 1.5 kgf - 0.9 kgf = 0.6 kgf

3. **Convert Upthrust to Newtons (if necessary):**
- Since 1 kgf = 9.81 N, we can convert the upthrust to Newtons:
- U = 0.6 kgf × 9.81 N/kgf = 5.886 N (this step is optional for relative density calculation)

4. **Calculate the Volume of the Solid:**
- The volume of the solid (V) can be calculated using the upthrust:
- The upthrust is equal to the weight of the liquid displaced, which can be expressed as:
- U = ρ_liquid × V × g
- Rearranging gives us:
- V = U / (ρ_liquid × g)
- Using the upthrust in kgf:
- V = 0.6 kgf / (1.2 × 10^3 kg/m³ × 9.81 N/kgf)
- V = 0.6 / (1.2 × 9.81) = 0.5 × 10^(-3) m³

5. **Calculate the Density of the Solid:**
- Density of the solid (ρ_solid) = Mass / Volume
- The mass of the solid can be calculated from its weight in air:
- Mass = WA / g = 1.5 kgf / 9.81 N/kgf = 0.152 kg (this step is optional for relative density calculation)
- Now, using the volume calculated:
- ρ_solid = 1.5 kgf / (0.5 × 10^(-3) m³)
- ρ_solid = 3 × 10^3 kg/m³

6. **Calculate the Relative Density:**
- Relative Density (R.D.) = Density of the solid / Density of water
- Density of water = 1 × 10^3 kg/m³
- R.D. = ρ_solid / ρ_water = (3 × 10^3 kg/m³) / (1 × 10^3 kg/m³) = 3

### Final Answer:
The relative density of the solid is **3** (no units).

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