1.

A metal ball immersed in alcohol weights W_(1)" at "0^(@)C and W_(2)" at "59^(@)C. The coefficient of cubic expansion of metal is less than that of alcohol. If the density of the mnetal is large compared to that of alcohol then:

Answer»

`W_(1)=W_(2)`
`W_(1) gt W_(2)`
`W_(1) lt W_(2)`
`W_(2)=(W_(1))/(2)`

Solution :Suppose that `V_(0)` is the volume of metal at `0^(@)C and V_(T)` is its volume at `T^(@)C`.
`therefore` Upthrust at temperature T is GIVEN by `U_(T)=V_(T)P_(T)g" where "P_(T)` is density of ALCOHOL at temperature T.
Since `V_(T)=V_(0)(1+gamma T) and P_(T) =(P_(0))/(1+gamma T)`
`therefore U_(T) =V_(0) (1+ gamma T) xx (P_(0))/(1+gamma T) CDOT g =V_(0) P_(0)g`
`U_(T)=U_(0)" where "U_(0)` is thrust at `0^(@)C`.
Since upthrust is independent of temperature
`therefore W_(1)=W_(2)`
THUS, correct choice is (a).


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