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A cemented sphere of radius R has a cavity of radius r which is packed with sawdust. The relative density of cement and sawdust are 2.4 and 0.3 respectively. Find the ratio of mass of cement to sawdust for which the sphere will float in water in completely submerged state.

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answer is 4.

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Detailed Solution

mass of cement =43πR3−r3×2.4ρwmass of sawdust=43πr3×0.3pwfor floating mg=Vρwg43πR3−r3×2.4ρw+43πr3×0.3ρw =43πR 3 ×ρw1.4R3=2.1r3 R3r3=32 mcms=43πR3−r3×2.4ρw43πr3×0.3ρw mcms=32−1×8=4

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A cemented sphere of radius R has a cavity of radius r which is packed with sawdust. The relative density of cement and sawdust are 2.4 and 0.3 respectively. Find the ratio of mass of cement to sawdust for which the sphere will float in water in completely submerged state.