A glass vessel is filled up to 3/5th of its volume by mercury. If the volume expansivities of glass and mercury be `9xx 10^(-6)//^(@)C` and `18xx10^(-5)//^(@)C` respectively, then the coefficient of apparent expansion of mercury is

Options

A. `17.1xx10^(-5)//^(@)C`
B. `9.9xx10^(-5)//^(@)C`
C. `17.46xx10^(-5)//^(@)C`
D. `16.5xx10^(-5)//^(@)C`

Answer

D

Explanation

Let V be the volume of the glass vessel. Then volume of mercury will be `(3//(5)` V.
Expansion of mercury`=(3//5)Vxxgamma_mDeltaT`
And that of glass`=Vgamma_gDeltaT`
Net (effective or apparent) expansion of mercury
`DeltaV=V((3gamma_m)/(5)-gamma_g)DeltaT`
`:.` Coefficient of apparent expansion will be
`(DeltaV)/((3//5)VxxDeltaT)=((3)/(5)gamma_mgamma_g)(5)/(3)`