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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?


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Solution

Step 1: Given data

  1. The weight of the body is W.
  2. The upthrust experienced by the body is R.

Step 2: Concept and formulae

  1. We know from the concept of Archimedes's principle that, when a body is fully or partially in a fluid, the upward thrust force (buoyancy force) experienced by a body equals the weight of the displaced fluid by the body.
  2. In this case, theapparentweightofthebody(W')=weightofthebody(Vgρ)-upthrust(Vgρ').
  3. If ρ and ρ' are the densities of water and the body, then the apparent weight of the body due to upthrust is W'=Vgρ-Vgρ' and the apparent density is ρa=ρ-ρ', where, V is the volume of the body, g is the acceleration due to gravity.

Step 3: Finding the apparent weight and apparent density

Now, according to the question, W>R.

We know,

apparentweight=bodyweight-upthrust

So, the apparent weight of the body is,

orW'=W-RorW'=Vgρ-Vgρ'

And the apparent density is,

ρa=ρ-ρ'

Therefore, the apparent weight is W-R and apparent density of the body is (ρ-ρ').


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