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.

Options

A. `(1)/(36200)//^(@)C`
B. `(1)/(43200)//^(@)C`
C. `(1)/(54100)//^(@)C`
D. `(1)/(23200)//^(@)C`

Answer

B

Explanation

`W_(0)=mg = 46 gm`
at `theta_(1) = 27^(@)C`
`W_(1) = 30 gm = w_(0)-B_(1)`
`B_(1) = 46-30`
`B_(1) = 16 = V_(1)rho_(1)g`
at `theta_(2)=42^(@)C rArr W_(2) = 30.5 gm = W_(0)-B_(2)`
`B_(2) = 15.5=V_(2)rho_(2)g :. (B_2)/(B_1) = (V_(2)p_(2))/(V_(1)p_(1))`
` (15.5)/(16) = (1+3 alpha_(s)xx15)xx1.2/1.24`
`alpha_(s) = [((15.5)/(16)xx(1.24)/(1.2))-1]xx1/45`
`alpha_(s) = 2.31xx10^(-5)//^(@)C = 1/43200`.