A body is volume `100cm^(3)` weighs 5 kgf in air. It is completely immersed in a liquid of density `1.8xx10^(3)kgm^(-3)`. Find (i) the upthrust due to liquid and (ii) the weight of the body in liquid.

Answer

To solve the problem step by step, we will first calculate the upthrust (buoyant force) acting on the body when it is immersed in the liquid, and then we will determine the weight of the body when it is submerged.

### Step 1: Convert the Volume of the Body to Cubic Meters
The volume of the body is given as \(100 \, \text{cm}^3\). We need to convert this volume into cubic meters for our calculations.

\[ \text{Volume in } m^3 = 100 \, \text{cm}^3 \times \left( \frac{1 \, m^3}{10^6 \, cm^3} \right) = 100 \times 10^{-6} \, m^3 = 1.0 \times 10^{-4} \, m^3 \]

### Step 2: Identify the Density of the Liquid
The density of the liquid is given as \(1.8 \times 10^3 \, \text{kg/m}^3\).

### Step 3: Calculate the Upthrust (Buoyant Force)
According to Archimedes' principle, the upthrust (buoyant force) can be calculated using the formula:

\[ \text{Upthrust} = \text{Volume of the body} \times \text{Density of the liquid} \times g \]

However, since we are given the weight of the body in kgf (kilogram-force), we will calculate the upthrust in kgf as well. The acceleration due to gravity \(g\) is already accounted for in kgf.

\[ \text{Upthrust} = \text{Volume} \times \text{Density} = (1.0 \times 10^{-4} \, m^3) \times (1.8 \times 10^3 \, \text{kg/m}^3) = 0.18 \, \text{kgf} \]

### Step 4: Calculate the Weight of the Body in Liquid
The weight of the body in liquid can be calculated by subtracting the upthrust from the weight of the body in air.

\[ \text{Weight in liquid} = \text{Weight in air} - \text{Upthrust} \]

Given that the weight of the body in air is \(5 \, \text{kgf}\):

\[ \text{Weight in liquid} = 5 \, \text{kgf} - 0.18 \, \text{kgf} = 4.82 \, \text{kgf} \]

### Final Answers
(i) The upthrust due to the liquid is \(0.18 \, \text{kgf}\).

(ii) The weight of the body in the liquid is \(4.82 \, \text{kgf}\).

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