Question

A body of mass 2kg and density 8000kg per metre cube is completely dipped in a liquid of density 800kg per metre cube. Find the force of buoyancy on it.

Answer 1

the buoyancy force exerted by a liquid on an object dipped in it will be

F = ρgV

where ρ is the density of the liquid, V is th volume of the object immersed in the liquid and g is the acceleration due to gravity.
So
here

ρ = 800 kg/m3

g =10 m/s2

and V = mass/density = 2/8000 = 2.5 X 10-4 m3

thus,

F = 800 X 10 X 2.5 X 10-4 = 8 X 2.5 X 10-1

or

F = 2 N

Answer 2

Heya user !!

Here's the answer you are looking for

☛Buoyant force = Upthrust = mass of liquid displaced.

Now, we know,
$density \: = \frac{mass}{volume} \\ \\ mass = density \times volume$
So,

☛ Mass of liquid displaced = Volume of liquid displaced × density of the liquid

By Archimedes principle, we know that when an object is partially or completely immersed in a liquid then the volume of liquid displaced is equal to the volume of immersed part of the object.

So,
☛ Volume of liquid displaced = Volume of the body

➡️Mass of body = 2kg
and it's density = 8000kg/m³

$d = \frac{m}{v} \\ \\ 8000 = \frac{2}{v} \\ \\ v = \frac{2}{8000} = \frac{1}{4000} {m}^{3}$

$So, \: volume \: of \: water \: displaced \: is \: \frac{1}{4000} {m}^{3}$

Thus, mass of water displaced
= volume of liquid displaced × density of liquid
$= \frac{1}{4000} \times 800 \\ \\ = \frac{2}{10} \\ \\ = 0.2kg$
Therefore, the upthrust or buoyant force

$= mass \times accl. \: due \: to \: gravity \\ = 0.2 \times 9.8 \\ = 1.96 \: kgm {s}^{ - 2}$
➡️ Therefore, the force is 1.96N


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