A sphere consists of concrete (relative density 2.4) with a sand-filled cavity (relative density 0.3). It floats entirely submerged. Find ratio of concrete mass to sand mass.
Physics · Mixed Chapter
JEE Main Practice

Question

A sphere consists of concrete (relative density 2.4) with a sand-filled cavity (relative density 0.3). It floats entirely submerged. Find ratio of concrete mass to sand mass.

G1 Physics · Accepted Answer

Step 1 — Let volume of concrete be Vc and sand volume Vs. Total displaced water volume is Vc + Vs at full immersion. Step 2 — Neutral flotation requires 2.4ρwVc + 0.3ρwVs = ρw(Vc + Vs). Step 3 — Rearrange: 1.4Vc = 0.7Vs ⇒ Vs = 2Vc. Step 4 — Mass ratio Mc/Ms = (2.4Vc)/(0.3 × 2Vc) = 4.