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A solid body floats in a liquid at a tem...

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`.

Text Solution

Verified by Experts

At `50^@ C`, density of solid = density of liquid.
At `06@ 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 %`.
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