A metal ball immersed in alcohol weights `W_1` at `0^@C` and `W_2` at `50^@C`. The coefficient of expansion of cubical the metal is less than that of the 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)`