A sphete of deamrter 7.0 cm and mass 266.5 g float in a bath of liquid. As the temperature is raised, the sphere begins to sink at a temperature of `35^@ C`. If the density of liqued is `1.527 g cm^(-3)` at` 0^@C`, find the coeffiecient of cubical expamsion of the liquid. Neglect the expansion of the sphere.

Explanation

Given : expansion of sphere is negligible
Density of liquid at `0^(@)C` , `p_(0)=1.527g//cc`
At the situation of sink,
Density of liquid=Density of sphere `p_(35)=(266.5)/((4)/(3)pi(3.5)^(3))=1.484g//"c c"`
`p_(35)=(p_(0))/(1+gamma(35-0))`
`1+35gamma=(p_(0))/(p_(35))=(1.527)/(1.484)=1.029`
`gamma=(0.029)/(35)=8.28xx10^(-4)//^(@)C` .