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

Options

A. `(f_(1)-f_(2))/(f_(2)t_(1)-f_(2)t_(1))`
B. `(f_(1)-f_(2))/(f_(2)t_(1)-f_(2)t_(1))`
C. `(f_(1)+f_(2))/(f_(2)t_(1)+f_(2)t_(1))`
D. `(f_(1)+f_(2))/(f_(2)t_(1)+f_(2)t_(1))`

Answer

A

Explanation

`W+p_(t_1)f_(1)Vg=rho_(t_(2))f_(2)vg`
`rho_(t_(1))f_(1)=rho_(t_(2))f_(2)`
`(rho_(0)/(1+gammat_(2)))f_(1) =(rho_(0)/(1+gammat_(0)))f_(2)`
`(1+gammat_(2))f_(1)=(1+gammat_(1))f_(2)`
`f_(1)-f_(2)=(f_(2)t_(1)-f_(1)t_(2))`
`gamma=(f_(1)-f_(2))/(f_(2)t_(1)-f_(1)t_(2))`