A metallic bob weights `50 g` in air. If it is immersed in a liquid at a temperature of `25^@ C`, it weights `45 g` . When the temperature of the liquid is raised to `100^@ C`, it weights `45.1 g`. Calculate the coefficient of cubical expansion of the liquid. Given that coefficient of cubical expansion of the metal is `12 xx 10^(-6) .^@ C^-1`.

Options

A. `1.3 xx 10^(-3) //""^(@)C`
B. `5.2 xx 10^(-3) // ""^(@)C`
C. `2.6 xx 10^(-3)//""^(@)C`
D. `0.26 xx 10^(-3)//""^(@)C`

Answer

C

Explanation

`V_(30^@C) = ("Loss of weight")/("Specific gravity" xx g) = ((45 - 25)g)/(1.5 xx g) = 13.33 cm^(3)`
`V_(40^@ C) = ((45 - 27) xx g)/(1.25 xx g) = 14.40 cm^3`
`therefore V_(40) = V_(30) [ 1 + gamma (Delta T)]`
`rArr gamma = (V_40 - V_30)/(V_30 (t_2 -t_1)) = (14.4 - 13.33)/(13.33 (40-30)) = 8.03 xx 10^(-3)//""^(@)C`
`therefore alpha = (gamma)/(3) = (8.03 xx 10^(-3))/(3) = 2.6 xx 10^(-3) //""^(@)C`