A body, at `4^(@)C,` floats with 0.98 part of its volume immersed in water. At what temperature the body will just immerse in water? Coefficient of real expansion of water `=3.3 times 10^(-4@)C^(-1).` Neglect expansion of the solid body.

Explanation

Let the required temperature be `t^(@)C`, and the volume of the body = V.
Let the densities of water at `4^(@)C` and `t^(@)C " be " d_(1) " and " d_(2)` respectively.
`therefore` From the condition of floatation, `V times 0.98 times d_(1)=V times d_(2)`
`therefore " "d_(1)/d_(2)=1/0.98=50/49`
As `" "d_(1)=d_(2){1+3.3 times 10^(-4)(t-4)},`
`" "d_(2)/d_(2){1+3.3 times 10^(-4)(t-4)}=50/49`
`therefore " "3.3 times 10^(-4) times (t-4)=-50/49-1=1/49`
`therefore " "t=1/(49 times 3.3 times 10^(-4))+4=61.84+4=65.84^(@)C.`