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9.1 , fluid mechanics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics9.1 , fluid mechanics1 Mark
MCQ
A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density $0.8$ and with its vertex submerged. When another liquid of relative density $\rho$ is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is $0.10$ $m$ and the radius of the circular base is $0.05$ $m$. The specific gravity $\rho$ is given by
  • A
    $1.0$
  • B
    $1.5$
  • C
    $2.1$
  • ✓
    $1.9$
✓

Answer

Correct option: D.
$1.9$
d
$h=0.1 \mathrm{m}$

By force balance

$\mathrm{mg}=0.8\left(\frac{1}{3} \pi\left(\frac{0.05}{3}\right)^{2}\left(\frac{\mathrm{h}}{3}\right)\right)$   $...(i)$

When liquid is added

$\mathrm{Mg}+\rho\left(\frac{1}{3} \pi\left(\frac{0.05}{3}\right)^{2}\left(\frac{\mathrm{h}}{3}\right)\right)$

$=0.8\left(\frac{1}{3} \pi\left(\frac{0.05}{2}\right)^{2}\left(\frac{\mathrm{h}}{2}\right)\right)$  $...(ii)$

By $(i)$ and $(ii)$

$(0.8)\left(\frac{1}{3} \pi \frac{(0.05)^{2} h}{3^{3}}\right)+\rho\left(\frac{1}{3} \pi \frac{(0.05)^{2} h}{3^{3}}\right)$

$=0.8\left(\frac{1}{3} \pi \frac{(0.05)^{2} h}{2^{3}}\right)$

$\frac{0.8+p}{3^{3}}=\frac{0.8}{8}=0.1$

$0.8+\rho=2.7$

$\rho=1.9$

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