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A vessel contains oil (density = 0.8 gm/cm³) over mercury (density = 13.6 gm/cm³). A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of sphere in gm/cm³ is:
Option: 1
3.3

Option: 2
6.4

Option: 3
7.2

Option: 4
12.8

Answers (1)

best_answer

Net force on the body -

$F_{B}+F_{v}= W$

$\rightarrow 6\pi \eta rv+\frac{4}{3}\pi r^{3}\sigma g= \frac{4}{3}\pi r^{3}\rho g$

$\rightarrow 6\pi \eta rv=\frac{4}{3}\pi r^{3} g\left ( \rho -\sigma \right )$

$\rightarrow v_{t}=\frac{2}{9}\frac{ r^{2} \left ( \rho -\sigma \right )}{\eta }g$

- wherein

$F_{B}-Buoyant \: force$

$F_{v}-viscous \: force$

$w-weight$

$\rho \rightarrow density \: of \: ball$

$\sigma \rightarrow density \: of \: water$

$V_{T} =terminal \: velocity$

Here viscous force is zero

Weight = Buoyant force

$Vp_{m}g=\frac{V}{2}p_{Hg}g+\frac{V}{2}p_{oil}g$

$p_{m}g=\frac{p_{Hg}+p_{oil}}{2}=\frac{13.6+0.8}{2}=\frac{14.4}{2}=7.2$

Posted by

himanshu.meshram

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