A cubical block of density ` rho ` floats completely immersed in two non-mixing liquids of densities ` rho _ 1 and rho _ 2 ` as shown in figure. The relation between ` rho , rho_1 and rho _ 2 ` is :

Options

A. ` rho = (1)/(2) (rho _1 + rho _2 ) `
B. ` rho = 2rho _ 1 + rho _ 2 `
C. ` rho = (1)/(3) (2 rho _ 1 + rho _ 2 ) `
D. ` rho = (1)/(2) (rho _1 + 2 rho _ 2 ) `

Answer

C

Explanation

Each side of the block=3x. For floating, weight of the block =upthrust due to liquid of density `rho_(1)+` upthrust due to liquid of density `rho_(2)`
`therefore" "(3x)^(3)pg=(3x)^(2)xx"2x"xxrho_(1)g+(3x)^(2)xx"x"xxrho_(2)gRightarrowrho=(1)/(3)(2rho_(1)+rho_(2))` Thus the correct choice is (C).