A metal ball immersed in alcohol weighs `w_(1) " at" 0^(@)C " and" w_(2) " at " 59^(@)C`. The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that

Options

A. `W_(1)gtW_(2)`
B. `W_(1)=W_(2)`
C. `W_(1)gtW_(2)`
D. none of these

Answer

C

Explanation

`W_(1)=mg-Vd_(a)g`
`W_(2)=mg-V^(')d_(a)^(')g`
`=mg-V(1+50gamma_(b))(d_(a)g)/((1+50gamma))`
`=mg-Vd_(a)g[(1+50gamma_(b))/(1+50gamma_(a))]`
`V=` volume of ball at `0^(@)C`
`d_(a)=` density of alcohool at `0^@C`
`V'=` volume of ball at `50^@C`
`d_(a)^'=`density of alcohol at `0^@C`
Given `gamma_(b)ltgamm_(a)`
`:. 1+50gamma_(b)lt1+50gamma_(a)`
`:.(1+50gamma_(b))/(1+50gamma_(b))lt1`
`:. W_(2)gtW_(1)` or `W_(1)gtW_(2)`