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

Hint: If the body of the weight is fully or partially in a fluid, the upward thrust is produced. According to Archimedes principle, the upward thrust force of the body equals the weight of the displaced fluid. The upward thrust force is also buoyancy force. The center of the upward thrust force and the center of gravity of the floating object should be the line on the same vertical plane. The apparent weight of the body and apparent density of the body is going to be found when the weight of the body is equal to the upthrust that it experiences in the water.

Formula used:
The apparent weight of the body on a fluid, ${W'} = {W_{body}} - {F_b}$
Where, ${W_{body}}$ - the weight of the body
$F_b$- buoyancy force or upward thrust force


Complete answer:
From the given, weight of the body ${W_{body}} = W$, upthrust force, ${F_b} = R$ and the condition is $W = R$
Substitute all the known values in the apparent weight formula,
${W'} = {W_{body}} - {F_b}$
${W'} = W - R$
After applying the condition$W = R$ in the above equation, we get
${W'} = R - R$
${W'} = 0$
Therefore, the value of the apparent weight of the liquid was calculated as zero.
If the apparent weight of the body in a liquid becomes zero, the apparent density of the body also becomes zero.

Note: The upward thrust force increases with increases in the density of the fluid. We know that seawater contains more density than freshwater, this is caused due to dissolved salts. so that we can swim more easily in the seawater than in the freshwater. When compared with water’s density, the relative density of the substance can be calculated. The relative density of the substance must be less than $1$, for the object to float on water. Otherwise, the relative density less than $1$, the object will sink in the water.