A metal ball immersed in alcohol weighs `w_(1) " and" 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) gt W_(2)`
B. `W_(1)=W_(2)`
C. `W_(1) lt W_(2)`
D. `W_(1)=(W_(2)//2)`

Answer

C

Explanation

The upthrust is given by `(4)/(3)pi R_(t)^(3)rho g`
Here `R_(t)^(3)=R_(0)^(3)(1+gamma_(m)t) and rho_(t)=rho_(0)//(1+gamma_(a)t)`
So, the upthrust at `t^(@)C` is given by
`=(4)/(3)pi R_(0)^(3)(1+gamma_(m)t)xx{rho_(0)//(1+gamma_(a)t)}g`
As `gamma_(m)lt gamma_(a)`, hence upthrust at `t^(@)C lt ` upthrust at `0^(@)C`
So, the upthrust is decreased. Hence weight in liquid gets increased.