If the density of ice is `0.9gcm^(-3)`, what portion of an iceberg will remain below the surface of water in a sea? (Density of sea water `=1.1gcm^(-3)`)

Explanation

Volume of the iceberg = `V "cm"^3`
Volume under sea water = `V_1`
Density of ice = `0.9 "g cm"^(-3)`
`therefore` Mass of iceberg = 0.9V g
Weight of iceberg = 0.9V gf
Density of sea water = `1.1 "g cm"^(-3)`
Mass of displaced sea water = `1.1 V_1` gf
Weight of displaced sea water = 1.1 `V_1` gf
`therefore` Upthrust = 1.1 `V_1` gf
According to law of flotation,
Weight of iceberg = Upthrust exerted by water
0.9 V / 1.1 `V_1`
`therefore V_1//V=9//11`
So, `9//11^(th)` part of the original volume of the iceberg will be under sea water.