Question

A body weighs W, in a liquid of density P1 and W2 in a liquid of density P2. What is the weight of body in a liquid of density P3 ?

please give answer with explanation​

Answer 1

Answer:

let m be the mass of the body, V be its volume and ρρ be its density. So V=m/ρV=m/ρ.

Weight of body in air, W=mgW=mg.

Effective weight of the body when completely immersed in a liquid of density ρ1ρ1 is

W1=mg−Vρ1g=mg−mρρ1gW1=mg-Vρ1g=mg-mρρ1g

=mg(1−ρ1ρ)=W(1−ρ1ρ)=mg(1-ρ1ρ)=W(1-ρ1ρ) ...(i)

similarly, W2=W(1−ρ2ρ)W2=W(1-ρ2ρ) ..(ii)

and W3=W(1−ρ3ρ)W3=W(1-ρ3ρ) ..(iii)

Using (i),(ii) and (iii) , we get

W3=W2(ρ3−ρ1)−W1ρ