A solid floats in a liquid at `20^@`C with 75 % of it immersed. When the liquid is heeated to `100^@`C, the same solid floats with `80%` of it immersed in the liquid. Calculate the coefficient of expansion of the liquid. Assume the volume of the solid to be constant.

A solid floats in a liquid at `20^@`C with 75 % of it immersed. When t

1.	A solid floats in a liquid at `20^@`C with 75 % of it immersed. When the liquid is heeated to `100^@`C, the same solid floats with `80%` of it immersed in the liquid. Calculate the coefficient of expansion of the liquid. Assume the volume of the solid to be constant.
Answer» Let m be the mass of the solid and V its volume. By the law of floatation Weight of floating object = Buoyant force In Case I: `mg=((3)/(4)V)rho_(20)g` Where `rho_(20)=` density of liquid at `20^@`C In Case II : `mg=((8)/(100)V)rho_(100)g`, Where `rho_(100)=`density of liquid at `100^@`C Considering both the cases `implies(3)/(4)rho_(20)=(4)/(5)rho_(100)implies(3)/(4)(rho_0)/(1+gammaxx20)=(4)/(5)(rho_0)/(1+gammaxx100)` After solving we get `gamma=(1)/(1180)=8.47xx10^(-4)//^(@)C`

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A solid floats in a liquid at `20^@`C with 75 % of it immersed. When the liquid is heeated to `100^@`C, the same solid floats with `80%` of it immersed in the liquid. Calculate the coefficient of expansion of the liquid. Assume the volume of the solid to be constant.

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