Two non-mixing liquids of densities ρ and nρ (n 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p

Question

Two non-mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal to : (A)  2 + (n + 1) p ρ (B)  2 + (n - 1) p ρ (C)  1 + (n - 1) p ρ (D)  1 + (n + 1) p ρ

Tardigrade Admin · Accepted Answer

LAdg = (1 - p) LA ρ g + pLAn ρ g d = (1 - p) ρ + np ρ d = ρ [L - p + np) d = ρ 1 + (n - 1) p

${2 + (n + 1) p} ρ$

${2 + (n - 1) p} ρ$

${1 + (n - 1) p} ρ$

${1 + (n + 1) p} ρ$

$L A d g = (1 - p) L A ρ g + p L A n ρ g$
$d = (1 - p) ρ + n pρ$
$d = ρ [L - p + n p)$
$d = ρ 1 + (n - 1) p$

Q. Two non-mixing liquids of densities ρ and nρ(n>1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL(p<1) in the denser liquid. The density d is equal to :

{2+(n+1)p}ρ

{2+(n−1)p}ρ

{1+(n−1)p}ρ

{1+(n+1)p}ρ

LAdg=(1−p)LAρg+pLAnρg d=(1−p)ρ+npρ d=ρ[L−p+np) d=ρ1+(n−1)p

${2 + (n + 1) p} ρ$

${2 + (n - 1) p} ρ$

${1 + (n - 1) p} ρ$

${1 + (n + 1) p} ρ$

$L A d g = (1 - p) L A ρ g + p L A n ρ g$
$d = (1 - p) ρ + n pρ$
$d = ρ [L - p + n p)$
$d = ρ 1 + (n - 1) p$