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_(1)//2)`

Answer

C

Explanation

Upthrust = (volume of metal ball)`xx` (density of liquid)`xx g` with increase in temperature volume of ball will increase and density of liquid will decrease.
But coefficient of cubical expansion of liquid is more.
Hence second effect is more dominating.
Therefore upthrust, at higher temperatures will be less or apparent weight will be more.