A sphere of diameter 7 cm and mass `265.5` gm floats in a bath of a liquid. As the temperature is raised, the sphere just begins to sink at a temperature of `35^(@)C`. If the density of a liquid of `0^(@)C` is `1.527`gm/cc, then neglecting the expansion of the sphere, the coefficient of cubical expansion of the liquid is

Explanation

The sphere will sink in the liqued at `35"^(@)C,` when its density becomes equal to the density of liquid at `30"^(@)C.` The density of sphere,
`P_(35)=(Mass)/(Volume)=(266.5)/((4)/(3)xx((22)/(7))xx((7)/(2))^(3))=1.483g//cm^(3)`
Now`" " P_(o)=P_(35)[1+gammaDeltaT]`
`1.527=1.483[1+gammaxx35]`
`1.029=1+gammaxx35`
`gamma=(1.209-1)/(35)=0.00083//"^(@)C`