A piece of metal weighs 46 g in air and 30 g in liquid of density `1.24 xx 10^3 kg m^(-3)` kept at `27^0C`. When the temperature of the liquid is raised to `42^0C`, the metal piece weights 30.5 g . The density of the liquid at `42^0 C` is `1.20 xx 10^3 kg m^(-3)`. Calculate the coefficient of linear expansion of the metal.

Options

A. `(1.4xx10^(-5))/("^(@)C)`
B. `(2.3xx10^(-5))/("^(@)C)`
C. `(4.3xx10^(-5))/("^(@)C)`
D. `(3.4xx10^(-5))/("^(@)C)`

Answer

B

Explanation

Change in weight = Upthrust (F)
where `" "F=V_(s)p_(t)g`
`rArr" "F'= V_(s)p_(t)'g`
`" "(F')/F=(V_(s)')/V_(s).(p_(l)')/(p_(l))or(F')/(F)=(1+gamma_(s)Delta theta)(p_(l'))/(p_(l))`
`((46-30.6)/(46-30))=(1+3xx alpha_(s)xx15)((1.20)/(1.24))`
or `" "alpha_(s)=2.3xx10^(-5)//^(@)C`