Whenever
a body is placed in a fluid, the fluid applies resultant up ward directional
force on the body and it is called up thrust. It’s numerical value which is the
product of volume of the fluid displaced, density of the fluid and acceleration
due to gravity at the given place.Volume of the fluid displaced it depends on
portion of the body that is there in the fluid. When the body is completely
immersed in the fluid volume of the fluid displaced is equal to the volume of
the body itself. When the body is partially immersed in the fluid , volume of
the fluid displaced equal to the volume of the body that is there inside the
fluid.

According
to Archimedes principle ,up thrust is
equal to the weight of the fluid displaced by a static fluid.

Basing
on this concept we can find out the relative density of a solid as well as a
fluid. Relative density of the fluid is equal to the ratio of the weight of the
body in air to the loss of the weight of the body in water.

Relative
density of the fluid can be determined as the ratio of loss of the weight of
the body in a liquid of the loss of the weight of the body in water.

Up
thrust depends on the density of the fluid. As density of the sea water is more
than that of ordinary water, upthrust in the case of the sea is more than that
of river. Upthrust also depends on acceleration due to gravity. If the
arrangement is placed in a lift and the lift is moving in upward direction than in the place of the
acceleration ,we have two consider both acceleration due to gravity as well as
the acceleration of the lift.

Under
different circumstances we can choose to the equation summed up thrust as shown
below.

**Determining the volume of the cavity**

Let
us consider a body having some cavity inside. We can calculate the value of upthrust when it is immersed in water. In the case of the volume of the fluid
with can write the volume of the body and in the case of the density of the
fluid we can write the density of water. Therefore we can get the volume of the
body is the ratio of upthrust to the density of the water and gravity as
shown.

Upthrust is nothing but the difference in the weight of the body near to the
weight of the body in water. By substituting this terms we can get the volume
of the cavity as shown below.

**Problems on up thrust**

Whenever
a body is in a fluid, the fluid applies upthrust, force in the upward
direction. The direction of top thrust is always the same. Depending on the
volume of the body inside the fluid up thrust will change.

**Problem one**

A
body is floating in water such that 6/10 parts of its volume is under water
what is the density of the body?

In
solving this problem we have to consider that weight of the body is equal to upthrust as the body is an equilibrium state. In the place of the volume of the
fluid displaced, we have to write only
six by 10

^{th}of the volume of the body cause only that much of the bodies inside the water.**Problem two**

Two
solids A and B float on water. It is observed that A floats with half of its
volume inside water and B floats with
2/3 its volume immerse it find the ratio
of their densities ?

Even
in solving this problem also we are having the same approach. The simple
concept is when the body is an equilibrium state the weight acting in the
downward direction is equal to the up thrust acting in the upward direction.

**Problem three**

A cubicle block of wood with each side a 10 cm long floats are at the interface
of water and oil. The lower surface is 2 cm below the interface of the liquid.
The height of oil and water columns each are 10 cm. Density of the oily is 0.8
g per cc then what is the mass of block ?

In
this problem the weight of the body is equal to the upthrust provided by both
water and oil. In the case of the water volume of the fluid displaced is equal
to 2 by 10

^{th}of the volume of the total body whereas in the case of the oil volume of the fluid displaced is equal to 8 by 10^{th}of the total volume of the body. The problem can be solved as shown below.
It is
the study of behavior of liquids in motion.

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