Question

A solid whose volume does not change with temperature floats in a liquid. For two different temperatures `t_1` and `t_2` of the liqiud, fraction `f_1` and `f_2` of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to
A. `(f_1-f_2)/(f_2t_1-f_1t_2)`
B. `(f_1-f_2)/(f_1t_1-f_2t_2)`
C. `(f_1+f_2)/(f_2t_1+f_1t_2)`
D. `(f_1+f_2)/(f_1t_1+f_2t_2)`

Answer 1

Correct Answer - A
As with the rise in temperature the liquid undergoes volume expansion therefore the fraction of solid submerged in liquid increases.
Fraction of solid submerged at `t_1^@C=f_1=` volume of displaced liquid
`=V_0(1+gammat_1)` ..(i)
and fraction of solid submerged at `t_2^@=f_2=` volume of displaced liquid
`=V_0(1+gammat_2)` ..(ii)
From Eqs. (i) and (ii), `(f_1)/(f_2)=(1+gammat_1)/(1+gammat_2)`
`impliesgamma=(f_1-f_2)/(f_2t_1-f_1t_2)`