Question

A cube of solid material( volume a³) with density ρs is levitating between two liquids with density ρ1, ρ2 . Calculate the height h.

Answer 1

Answer:

Explanation:

there are two buoyancies here

one is exerted by p1 and another is exerted by p2

formula for buoyancy is vpg

buoyancy exterted by pi is v1p1g

v1=a*a*h

v2=a*a*a-h

now substitute in below

v1p1g+v2p2g = mg

v1p1g+v2p2g=vpg

v1p1+v2p2=vp

(a^3-ah)p1 + a^2hp2=(a^3)p

(a^3)p1-ahp1 +a^2hp2 = a^3p

a^3(p-p1) = h(a^2p2-ap1)

a^3(p-p1) / a^2p2-ap1 =h