A piece of metal weighs 46 g in air and 30 g in lipuid 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 liqued at `42^0 C` is `1.20 xx 10^3 kg m^(-3)`. Calculate the coefficient of linear expandsion of the metal.

Explanation

`W_0=mg=46gm`
At `theta_1=27^@C`
`W_1=30gm=w_0-B_1`
`B_1=46-30=16==V_1rho_1g`
at `theta_2=42^@CimpliesW_2=30.5gm=W_0-B_2`
`B_2=15.5=V_2rho_2g :. (B_2)/(B_1)=(V_2P_2)/(V_1p_1)`
`(15.5)/(16)=(1+3alpha_Sxx15)xx(1.2)/(1.24)`
`alpha_S=[((15.5)/(16)xx(1.24)/(1.2))-1]xx(1)/(45)`
`alpha_S=2.31xx10^(-5)//^(@)C=(1)/(43200)`