A body is floating in a beaker filled with water. $1 / 3^{rd}$ of the body is inside the water and $2 / 3^{rd}$ is in the air as shown in the figure. What will be the density of the body.
$ρ_{w} = Density of water$
$ρ_{b} = Density of the body$ [ $3 marks$ ]

Open in App

Solution

It is given that $1 / 3^{rd}$ of the body is submerged in the water.

So, the volume of displaced water,
$V_{w} = \frac{V}{3}$
where $V =$ Volume of the body

Using Archimedes' principle, the weight of the body is equal to the weight of water displaced by the body. [ $1 mark$ ]

$W_{b} = W_{w}$

$⟹ ρ_{b} V g = ρ_{w} V_{w} g$

$⟹ ρ_{b} V = ρ_{w} \frac{V}{3}$

$⟹ ρ_{b} = \frac{ρ_{w}}{3}$

Hence, the density of the body is $1 / 3^{rd}$ of the density of the water in the container. [ $2 marks$ ]

Suggest Corrections

Similar questions

Q. Body A of density

(ρ_{A})

is floating in the water. When another body B having density

(ρ_{B} = 1500 k g m^{- 3})

and same dimensions is placed on body A, then the system just sinks in the water. What fraction of body A was originally immersed in the water?
The density of water is

ρ_{w} = 1000 k g m^{- 3}

Q. A ship floats with

{\frac{1}{3}}^{r d}

of its volume outside. when its in water. When it floats in another liquid,

{\frac{2}{3}}^{r d}

of its volume is outside the liquid. What is the relative density of the liquid?
[

3 marks

]

Q. A body floats with

\frac{1}{3} r d

of its volume outside water and

\frac{3}{4} t h

of its volume outside liquid, then the density of the liquid is

Q. Body A is half immersed in the water. If another body with same dimentions is placed on body A, then what will be the density of body B (

ρ_{B}

) when the system is fully immersed in the water.
The density of water is

ρ_{w}

When an object floats on water and on a liquid with different volumes inside the water and inside the liquid .

Is the buoyant force acted by the water and the liquid equal?

for eg - A body floats with 1/3rd of its volume outside the water and 3/4th of its volume outside the liquid . what will be the density of the liquid ? is the buoyant force acted by the different fluids equal?

Join BYJU'S Learning Program

A body is floating in a beaker filled with water. 1/3rd of the body is inside the water and 2/3rd is in the air as shown in the figure. What will be the density of the body. ρw=Density of water ρb=Density of the body [3 marks]

A body is floating in a beaker filled with water. $1 / 3^{rd}$ of the body is inside the water and $2 / 3^{rd}$ is in the air as shown in the figure. What will be the density of the body.
$ρ_{w} = Density of water$
$ρ_{b} = Density of the body$ [ $3 marks$ ]