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. `7.6xx10^(-4@) C^(-1)`
B. `8.6xx10^(-4@) C^(-1)`
C. `7.3xx10^(-4@) C^(-1)`
D. `8.3xx10^(-4@) C^(-1)`

Answer

D

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)`