Question

# A body of weight $W$, experiences an upthrust $R$ in water. What will be the apparent weight of the body and the apparent density of the body when $W=R$?

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Solution

## Step 1. Given data:Weight of the body = $W$Upward thrust = $R$ Given condition, Weight of the body $W$ = upward thrust $R$ Archimedes's principle:If the weight of the body is fully or up to some limit in a fluid, an upward force is produced. According to Archimedes's principle, this upward force of the body is equal to the weight of the displaced fluid by the body. The upward thrust force is also known as 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.Step 2. Formula used:The apparent weight of the body on a fluid is given by, $W\text{'}={W}_{b}-{F}_{b}$…………$\left(1\right)$Where, ${W}_{b}$ =the weight of the body ${F}_{b}$- buoyancy force or upward thrust force,Step 3. Calculations:Here, weight of the body ${W}_{b}=W$, Upthrust force, ${F}_{b}=R$ Condition is $W=R$Substituting all the given values in $\left(1\right)$, $W\text{'}=W-R$…………..$\left(2\right)$Now as per given condition, $W=R$, Substituting the given condition in $\left(2\right)$ $W\text{'}=R-R=0$Therefore, the value of the apparent weight of the body is zero.If the apparent weight of the body becomes zero, the apparent density of the body automatically also becomes zero.Hence the apparent weight of the body and the apparent density of the body in this condition is zero.

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