A sphere of diameter `7 cm` and mass `266.5 g` floats in a bath of liquid. As the temperature is raised, the sphere just sinks at a temperature of `35^@ C`. If the density of the liquid at `0^@C` is `1.527 g//cm^3`, find the coefficient of cubical expansion of the liquid. ignore expansion of sphere.

Explanation

By the law of floatation
`266.5=(4pi)/(3)((7)/(2))^3xxrho_(35)`
where `rho_(35)=` density of the liquid at `35^@C`
`rho_(35)=1.4839(g)/(cm^3)`
But `rho_0=rho_(35)(1+gammaxx35)`
`1.527=1.4839(1+35gamma)=8.3xx10^(-4@) C^(-1)`