Question

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.

Answer 1

Correct Answer - C
The sphere will sink in the liquid at `35^@ C` when its density becomes equal to the dencity of liquid at `35^@ C`
The dencity of sphere,
`rho _35 =(266.5)/(4/3 xx ((22)/7) xx (7/2)^3`
= `1.483 g//cm^3`
Now, `rho _0 = rho_35[1 + gammaDeltaT)`
`1.527 = 1.483[1 + gamma xx 35]`
`1.029 = 1 + gamma xx 35`
`gamma =(1.029 - 1)/(35)`
= `0.00083//^@ C`.