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

The sphere will sink in the liquid at `30^(0)C`, when its density becomes equal to the density of liquid at `35^(0)C`. The density of sphere,
`rho_(1) = (m)/(V), V = (4)/(3)pir^(3)`
`rho_(t) = (266.5)/((4)/(3) xx ((22)/(7)) xx ((7)/(2))^(3)) = 1.483g // cm^(3)`
Now `rho_(@) = rho_(t)[1 + gammaDeltat]`
`1.527 = 1.483[1 + gamma xx 35], 1.029 = 1 + gamma xx 35`
` gamma = (1.029 - 1)/(35) = 0.00083//^(@)C`