Question

A body weighs 550gf in air and 370gf in water it is completely immersed in water. Find:

1. The upthrust on the body.
2. The volume of the body. $\left( {{\text{Density of water = }}1gc{m^{ - 3}}} \right)$

Answer 1

Whenever we weigh an object in air and then weigh the same object in water, we see that the weight in air is more than the weight in water, this is because water (fluid) applies an upward force on the object known as upward force. To know the upthrust of the body, calculate the water displaced by the body. To find out the volume of the body use mass-density formula.

Complete step by step solution:
Step 1:
Here, we need to find the upthrust on the body,
So, find the difference in the weight of the body:
${W_{net}} = 550 - 370$;
$\Rightarrow {W_{net}} = 180gf$;
According to Archimedes principle the upthrust on the body is equal to the weight of the water displaced by the body.
So, by the above principle the weight of the water that is displaced by the body$\left( {{W_{net}} = 180gf} \right)$is equal to the upthrust force.
${F_u} = {W_{net}} = 180N$;

Step 2: Finding out the volume of the body:
Apply mass-density formula:
$D = \dfrac{M}{V}$;
Here:
M = Mass;
V = Volume;
D = Density;
Writing the above equation in terms of volume:
$V = \dfrac{M}{D}$;
Put the given value in the above equation:
Here, the mass would be the net difference in the weight of the object.
$\Rightarrow V = \dfrac{{180}}{1}$;
$\Rightarrow V = 180g/cc$;

The upthrust on the body is 180N and the volume of the body is 180g/cc;

Note: Here, we need to first apply the Archimedes principle and equate the difference in weight of the body to the upward force or upthrust. The volume of the body would be the same as the weight of the water displaced by it, remember that it is only true with fluids whose density is $1gc{m^{ - 3}}$.