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STD 11 - 9.1 , fluid mechanics — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 9.1 , fluid mechanics4 Marks
MCQ
A sphere of solid material of relative density $9$ has a concentric spherical cavity and  floats having just sinked in water. If the radius of the sphere be $R$, then the radius of  the  cavity $(r)$ will be related to $R$ as :-
  • ✓
    $r^3 = \frac{8}{9} R^3$
  • B
    $r^3 = \frac{2}{3} R^3$
  • C
    $r^3 = \frac{\sqrt 8}{3} R^3$
  • D
    $r^3 = \sqrt { \frac{2}{3}} R^3$
✓

Answer

Correct option: A.
$r^3 = \frac{8}{9} R^3$
a
$\frac{4}{3} \pi\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right) \rho \mathrm{g}=\frac{4}{3} \pi \mathrm{R}^{3} \rho_{\mathrm{w}} \mathrm{g}$

$9\left(R^{3}-r^{3}\right)=R^{3}$

$r^{3}=\frac{8 R^{3}}{9}$

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