The density of the material of a hollow sphere of radius R is rho. Prove that the sphere can float on water if the thickness (t) of its wal satisfies the relation : tleR/(3rho).

The density of the material of a hollow sphere of radius R is rho. Pro

1.	The density of the material of a hollow sphere of radius R is rho. Prove that the sphere can float on water if the thickness (t) of its wal satisfies the relation : tleR/(3rho).
Answer» Solution :According to the condition of floatation, weight of the SPHERE `le` weight of the same volume of water or, `[4/3piR^(3)-4/3pi(R-t)^(3)]rhole4/3piR^(3)xx1` or, `[4/3piR^(3)-4/3piR^(3)(1-t/R)^(3)]rhole4/3piR^(3)` or, `4/3piR^(3)[1-(1-t/R)^(3)]rhole4/3piR^(3)` or, `[1-(1-(3t)/R)]rhole1""[tleR,"terms CONTAINING "t^(3)/R^(3),t^(2)/R^(2)" are neglected"]` or, `(3t)/Rrhole1or,tleR/(3rho)`.