When a liquid in a glass vessel is heated its apparent expansion is `10.30 xx 10^-4 //^@C` same liquid when heated in a metal its apparent expansion `10.06 xx10^-4//^@C`. The coefficient of linear expansion of the metal is (Coefficient of linear expansion of glass = `9 xx 10^-6 //^@C`)

Options

A. `51 xx 10^-6 //^@C`
B. `43 xx 10^-6 // ^@C`
C. `25 xx 10^-6 // ^@C`
D. `17 xx 10^-6 //^@C`

Answer

D

Explanation

`gamma_(r) = gamma_(a) + gmaa_(g) , gamma_(g)=3alpha`
For glass,`gamma_(r)= 10.30xx10^(-4) + 3xx9xx10^(-6)`
`=10.57xx10^(-4)//^@C`
For metal, `gamma_(r) = gamma_(a) + gamma_(m)`
`10.57xx10^(-4) = 10.06 xx 10x + 3(alpha_(m))`
`therefore alpha_(m) = 0.17xx10^(-4) = 17xx10^(-6)//^@C`