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.

Options

A. `0.0043//^(@)C`
B. `0.00083//^(@)C`
C. `0.00025//^(@)C`
D. `0.00010//^(@)C`

Answer

B

Explanation

The sphere will sink in the liquid at `35^(@)C,` when its density becomes equal to the density of at `35^(@)C.` The density of sphere,
`p_(35)=(266.5)/(3/4xx(22/7)xx(7/2)^(3))=1.483g cm^(-3)`
Now, `p_(o)=p_(35)[1+gammaDeltaT] rArr1.527=1.483[1+gammaxx35]`
`" "1.029 =1+gammaxx35`
`" "gamma=(1029-1)/35=0.00083//^(@)C`