A hollow sphere of radius R is made of metal whose specific gravity is ρ . The sphere will float in water if thickness of wall of sphere is (thickness of wall << R)

GivenRadius of hollow sphere =RSpecific gravity= ρNow mass of spherical shellM1= Solid volume of the sphere density of materialM1=4πR2tρ Where  M1=Mass of the hollow spheret=Thickness of the hollow sphereWhile the mass of water having same volume =  Whole volume of the sphere × density of the waterM2=43πR3ρw For the floatation of sphere  M1≤M2⇒4πR2tρ≤43πR3ρw ⇒tρ≤R3∵ρw=1 g/cm3 ∴  Thickness t≤R3ρ