A vessel contains oil (density 0.9 g cc- 1 ) over mercury (density 13.6 g cc- 1 ). A homogeneous sphere floats with one-third of its volume immersed in mercury and the rest immersed in oil. The density of the material of the sphere in g cc- 1 is

Question

A vessel contains oil (density 0.9 g cc- 1 ) over mercury (density 13.6 g cc- 1 ). A homogeneous sphere floats with one-third of its volume immersed in mercury and the rest immersed in oil. The density of the material of the sphere in g cc- 1 is (A) 3.3 (B) 6.4 (C) 5 text.1 (D) 12.8

Tardigrade Admin · Accepted Answer

For equilibrium, the total upward push will be equal to the downward pull. If

V

is the volume of the sphere, then we have

(\frac{V}{3}) (13.6) g + (\frac{2 V}{3}) (0 .9) g = V ρ g

∴ ρ = (\frac{13 . 6 + 1 . 8}{2}) (g cm)^{- 3} = 5 .1 (g cm)^{- 3}

Q. A vessel contains oil (density $0.9 g c c^{- 1}$ ) over mercury (density $13.6 g c c^{- 1}$ ). A homogeneous sphere floats with one-third of its volume immersed in mercury and the rest immersed in oil. The density of the material of the sphere in $g c c^{- 1}$ is

$3.3$

$6.4$

$5 .1$

$12.8$

For equilibrium, the total upward push will be equal to the downward pull. If $V$ is the volume of the sphere, then we have
$(\frac{V}{3}) (13.6) g + (\frac{2 V}{3}) (0 .9) g = V ρ g$
$∴ ρ = (\frac{13 . 6 + 1 . 8}{2}) (g cm)^{- 3} = 5 .1 (g cm)^{- 3}$

Q. A vessel contains oil (density 0.9gcc−1 ) over mercury (density 13.6gcc−1 ). A homogeneous sphere floats with one-third of its volume immersed in mercury and the rest immersed in oil. The density of the material of the sphere in gcc−1 is

3.3

6.4

5.1

12.8