A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 . For this sphere to float with its ent

Question

A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 . For this sphere to float with its entire volume submerged under water, ratio of mass of concrete to mass of sawdust will be :-

TestHub · Accepted Answer

For full submersion, buoyancy equals the total weight:
$B = ρ_{w} \frac{4 π R ^{3}}{3} g$
$W_{c} = ρ_{c} \frac{4 π ( R ^{3} - r ^{3} )}{3} g$
$W_{s} = ρ_{s} \frac{4 π r ^{3}}{3} g$
$B = W_{c} + W_{s}$
Using specific gravities 2.4 and 0.3:
$R^{3} = 2.4 (R^{3} - r^{3}) + 0.3 r^{3}$
$r^{3} = \frac{2}{3} R^{3}$
$\frac{m _{c}}{m _{s}} = \frac{2.4 ( R ^{3} - r ^{3} )}{0.3 r ^{3}} = 4$

Physics - Fluid Question with Solution | TestHub

Options:

Doubts & Discussion