A body weighs `W_(1)` in a liquid of density `rho_(1)` and `W_(2)` in a liquid of density `rho_(2)`. What is the weight of body in a liquid of density `rho_(3)`?

Explanation

The net force acting on a body completely immersed in a liquid of density d ,
` F = mg - F_(b) = mg - Vdg`
` = mg - m/D dg , ` where V = volume , m = mass & D d= density of the body .
` = mg(1-d/D)`
By putting `F = W_(1)` for the body when kept in first liquid , we obtain
`W_(1) = mg ( 1 - d_(1)/D)= W (1- d_(1)/D)" "`...(a)
Similarly, `W_(2) = mg (1 - (d_(2))/D)= W (1-d_(1)/D)" "`..... (b)
and `W_(3) = mg(1-d_(3)/D) = W (1-d_(3)/D) = " "` ...(c )
Using (a) , (b) & (c ) we obtain
`W_(3)= (W_(2)(d_(3)-d_(1))-W_(1)(d_(3)-d_(2)))/(d_(2) -d_(1)) `