question_answer

When a block of iron floats in mercury at \[0{}^\circ C\], fraction \[{{k}_{1}}\] of its volume is submerged, while at the temperature \[60 {}^\circ C\], 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 \[{{\operatorname{k}}_{1}}/{{k}_{2}}\]can be expressed as

A) \[\frac{1+60{{\gamma }_{Fe}}}{1+60{{\gamma }_{hg}}}\]

B) \[\frac{1-60{{\gamma }_{Fe}}}{1+60{{\gamma }_{Hg}}}\]

C) \[\frac{1+60{{\gamma }_{Fe}}}{1-60{{\gamma }_{Hg}}}\]

D) \[\frac{1+60{{\gamma }_{Fe}}}{1+60{{\gamma }_{Hg}}}\]