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

Let specific gravities of concrete and saw dust are  ρ1 and ρ2  respectively. According to principle of floatation weight of whole sphere = upthrust on the sphere 43πR3−r3ρ1g+43πr3ρ2g=43πR3×1×g⇒R3ρ1−r3ρ1+r3ρ2=R3⇒R3ρ1−1=r3ρ1−ρ2⇒R3r3=ρ1−ρ2ρ1−1⇒R3−r3r3=ρ1−ρ2−ρ1+1ρ1−1⇒R3−r3ρ1r3ρ2=1−ρ2ρ1−1ρ1ρ2⇒ Mass of concrete  Mass of saw dust =1−0.32.4−1×2.40.3=4