जब एक लोहे का ब्लॉक `0^(@)C` पर पारे में तैरता है तथा उसके आयतन का `k_(1)` भाग निमग्न रहता है, जबकि `60^(@)C` पर `k_(2)` भाग निमग्न रहता है। यदि लोहे व पारे के आयतन प्रसार गुणांक क्रमशः `gamma_(Fe)` व `gamma_(Hg)` हो तब अनुपात `k_(1)//k_(2)` होगा

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

`k_(1)=((rho_(Fe))/(rho_(Hg)))_(0^(@)C)` तथा `k_(2)=((rho_(Fe))/(rho_(Hg)))_(60^(@)C)`

जहाँ, `rho` = घनत्व
`therefore (k_(1))/(k_(2))=((rho_(Fe))_(0^(@)C))/((rho_(Hg))_(0^(@)C))xx((rho_(Hg))/((rho_(Fe))))_(60^(@)C)=((1+60gamma_(Fe)))/((1+60gamma_(Hg)))`
(i) `(rho_("ठोस"))/(rho_("द्रव"))`
(ii) `(rho_(theta^(@)C))/(rho_(0^(@)C))=(1)/(1+gammatheta)` (`because rho prop(1)/("आयतन")`, द्रव्यमान नियत है)
`therefore (rho_(theta^(@)C))/(rho_(0^(@)C))=(V_(0^(@)C))/(V_(theta^(@)C))=(V_(0^(@)C))/(V_(0^(@)C)+DeltaV)=(V_(0^(@)C))/(V_(0^(@)C)+V_(0^(@)C)gammatheta)=(1)/(1+gammatheta)`