A concrete sphere of radius fl has cavity of radius r which is packed with saw dust. The specific gravity of concrete and saw dust 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 saw dust will be

The weight of whole sphere will be equal to the upthrust' Hence43πR3−r3ρ1+43πr3ρ2=43πR3×1 where p1 and p2 are the specific Sravities of concrete and saw dust respectivelY  R3ρ1−r3ρ1+r3ρ2=R3  or R3ρ1−1=r3ρ1−ρ2 or R3r3=ρ1−ρ2ρ1−1 or R3−r3r3=ρ1−ρ2−ρ1+1ρ1−1 or R3−r3ρ1r3ρ2=1−ρ2ρ1−1×ρ1ρ2 or  Mass of concrete  Mass of saw dust =1−0⋅32⋅4−1×2⋅40⋅3=4