A body floats with one third of its volume outside water and three fourth of its volume, outside another liquid. The density of another liquid is:

Question

A body floats with one third of its volume outside water and three fourth of its volume, outside another liquid. The density of another liquid is: (A)  (9/4)gm/cm3  (B)  4.9 gm/cm3  (C)  (8/3)gm/cm3  (D)  (3/8)gm/cm3

Tardigrade Admin · Accepted Answer

Let V be the volume of the body. Weight of body is equal to weight of water displaced =2 / 3 ∨ × 1 × g In another liquid, weight of body =1 / 4 ∨ × ρ × g ∴ 2 / 3 ∨ g=1 / 4 ∨ ρ g or ρ=8 / 3 gm / cm 3

Q. A body floats with one third of its volume outside water and three fourth of its volume, outside another liquid. The density of another liquid is:

$\frac{9}{4} g m / c m^{3}$

$4.9 g m / c m^{3}$

$\frac{8}{3} g m / c m^{3}$

$\frac{3}{8} g m / c m^{3}$

Let $V$ be the volume of the body.
Weight of body is equal to weight of water displaced
$= 2/3 \lor \times 1 \times g$
In another liquid, weight of body
$= 1/4 \lor \times ρ \times g$
$∴ 2/3 \lor g = 1/4 \lor ρ g$
or $ρ = 8/3 g m / c m^{3}$

Q. A body floats with one third of its volume outside water and three fourth of its volume, outside another liquid. The density of another liquid is:

49​gm/cm3

4.9gm/cm3

38​gm/cm3

83​gm/cm3

Let V be the volume of the body. Weight of body is equal to weight of water displaced =2/3∨×1×g In another liquid, weight of body =1/4∨×ρ×g ∴2/3∨g=1/4∨ρg or ρ=8/3gm/cm3

$\frac{9}{4} g m / c m^{3}$

$4.9 g m / c m^{3}$

$\frac{8}{3} g m / c m^{3}$

$\frac{3}{8} g m / c m^{3}$

Let $V$ be the volume of the body.
Weight of body is equal to weight of water displaced
$= 2/3 \lor \times 1 \times g$
In another liquid, weight of body
$= 1/4 \lor \times ρ \times g$
$∴ 2/3 \lor g = 1/4 \lor ρ g$
or $ρ = 8/3 g m / c m^{3}$