Question

A body of weight W, experiences an upthrust R in water. What will be the apparent weight of the body and apparent density of the body when W>R?

Answer 1

Step 1: Given data

1. The weight of the body is $W$.
2. The upthrust experienced by the body is $R$.

Step 2: Concept and formulae

1. We know from the concept of Archimedes's principle that, when a body is fully or partially in a fluid, the upward thrust force (buoyancy force) experienced by a body equals the weight of the displaced fluid by the body.
2. In this case, $theapparentweightofthebody(W\text{'})=weightofthebody\left(Vg\rho \right)-upthrust(Vg\rho \text{'}).$
3. If $\rho$ and $\rho \text{'}$ are the densities of water and the body, then the apparent weight of the body due to upthrust is $W\text{'}=Vg\rho -Vg\rho \text{'}$ and the apparent density is ${\rho }_a=\left(\rho -\rho \text{'}\right)$, where, V is the volume of the body, g is the acceleration due to gravity.

Step 3: Finding the apparent weight and apparent density

Now, according to the question, $W>R$.

We know,

$apparentweight=bodyweight-upthrust$

So, the apparent weight of the body is,

$$\begin{gathered} orW\text{'}=W-R \\ orW\text{'}=Vg\rho -Vg\rho \text{'} \end{gathered}$$

And the apparent density is,

${\rho }_a=\left(\rho -\rho \text{'}\right)$

Therefore, the apparent weight is $\mathit{W}\mathbf{-}\mathit{R}$ and apparent density of the body is $\left(\rho -\rho \text{'}\right)$.