When a block of iron in mercury at `0^@C,` fraction `K_1`of its volume is submerged, while at the temperature `60^@C,` a fraction `K_2` is seen to be submerged. If the coefficient of volume expansion of iron is `gamma_(Fe)` and that of mercury is `gamma_(Hg),` then the ratio `(K_1)//(K_2)` can be expressed as

Options

A. `(1 + 60gamma_(Fe))/(1 + 60gamma_(Hg))`
B. `(1 - 60gamma_(Fe))/(1 + 60gamma_(Hg))`
C. `(1 + 60gamma_(Fe))/(1 - 60gamma_(Hg))`
D. `(1 + 60gamma_(Hg))/(1 - 60gamma_(Fe))`

Answer

A

Explanation

`Vdg = vrhog , ((v)/(v)) = (d)/(rho), k_(1) = (d_(1))/(rho_(1))` at `0^(0)C`
`k_(2) = (d_(2))/(rho_(2))` at `t^(0)C, (d_(1))/(d_(2)) (rho_(2))/(rho_(1))`
`(k_(1))/(k_(2)) = (d_(0)(1 + gamma_(Fe)t))/(d_(0)) xx (rho_(0))/((1 + gamma_(Hg)t)rho_(0)) = (1 + gamma_(Fe)t)/(1 + gamma_(Hg)t)`