A vessel contains oil (density =0.8 g / cm 3 ) over mercury (. density .=13.6 g / cm 3) . A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density (in g / cm 3 ) of the material of sphere is

Question

A vessel contains oil (density =0.8 g / cm 3 ) over mercury (. density .=13.6 g / cm 3) . A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density (in g / cm 3 ) of the material of sphere is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/f97faf4af8e4a30835b9ba3df71319df-.png" /> Weight = Buoyant force V ρm g=(V/2) ρ Hg g+(V/2) ρ oil g ρm=(ρ Hg +ρ oil /2) =(13.6+0.8/2)=(14.4/2)=7.2 g / cm 3

Q. A vessel contains oil (density $= 0.8 g / c m^{3}$ ) over mercury $($ density $= 13.6 g / c m^{3}) .$ A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density (in $g / c m^{3}$ ) of the material of sphere is

Weight $=$ Buoyant force
$V ρ_{m} g = \frac{V}{2} ρ_{H g} g + \frac{V}{2} ρ_{o i l} g$
$ρ_{m} = \frac{ρ _{H g} + ρ _{o i l}}{2}$
$= \frac{13.6 + 0.8}{2} = \frac{14.4}{2} = 7.2 g / c m^{3}$

Q. A vessel contains oil (density =0.8g/cm3 ) over mercury ( density =13.6g/cm3). A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density (in g/cm3 ) of the material of sphere is

Weight = Buoyant force Vρm​g=2V​ρHg​g+2V​ρoil​g ρm​=2ρHg​+ρoil​​ =213.6+0.8​=214.4​=7.2g/cm3

Q. A vessel contains oil (density $= 0.8 g / c m^{3}$ ) over mercury $($ density $= 13.6 g / c m^{3}) .$ A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density (in $g / c m^{3}$ ) of the material of sphere is

Weight $=$ Buoyant force
$V ρ_{m} g = \frac{V}{2} ρ_{H g} g + \frac{V}{2} ρ_{o i l} g$
$ρ_{m} = \frac{ρ _{H g} + ρ _{o i l}}{2}$
$= \frac{13.6 + 0.8}{2} = \frac{14.4}{2} = 7.2 g / c m^{3}$