The coefficient of volume expansion of glycerine is `49 xx 10^(-5)//^(@)C`. What is the fractional change in its density (approx.) for `30^(@)C` rise in temperature?

Options

A. `7.5 xx 10^(-2)`
B. `3.0 xx 10^(-2)`
C. `1.5 xx 10^(-2)`
D. `1.1 xx 10^(-2)`

Answer

C

Explanation

`gamma = 49 xx 10^(-5) K^(-1)`
`rho . = (rho)/(1 + gamma Delta theta) = (rho)/(1 + 49 xx 10^(-5) xx 30)`
Fractional change -
`(1 - (porp.)/(rho)) = (1- (1)/(1 + 49 xx 10^(-5) xx 30))`
`=0.0145 ~~ 1.5 xx 10^(-2)`