A solid body floats in a liquid at a temperature `t = 50^@ C` being completely submerged in it. What percentage of the volume of the body is submerged in the liquid after it is cooled to `t_0 = 0^@ C` if the coefficient of cubic expansion for the solid is `gamma_s = 0.3 xx 10^-5 .^@ C^-1` and of the liquid `gamma_l = 8 xx 10^-5 .^@ C^-1`.

Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

1.	A solid body floats in a liquid at a temperature `t = 50^@ C` being completely submerged in it. What percentage of the volume of the body is submerged in the liquid after it is cooled to `t_0 = 0^@ C`, if the coefficient of cubic expansion for the solid is `gamma_s = 0.3 xx 10^-5 .^@ C^-1` and of the liquid `gamma_l = 8 xx 10^-5 .^@ C^-1`.
Answer» At `50^@ C`, density of solid = density of liquid. At `[emailprotected] C` fraction submerged `((rho_s)/(rho _l))_(0^@ C) xx 100 ` …(i) `(rho)_(50) = (rho_0)/(1 + 50 gamma)` `:. rho_0 = rho _(50) (1 + 50 gamma)` Substituting in Eq. (i), we have ltbtgt % of fraction submerged =`((1 + 50 gamma_s)/(1 + 50 gamma_l)) xx 100 = ((1 + 0.3 xx 10^-5)/(1 + 8 xx 10^-5)) xx 100` = `99.99 %`.

Discussion