A glass rod when measured with a zinc scale, both being at `30^(@)C`, appears to be of length `100`cm . If the scale shows correct reading at `0^(@)C`, then the true length of glass rod at `30^(@)C` and `0^(@)C` are :-
(`alpha_("glass") = 8 xx 10^(-6)"^(@)C ^(-1), alpha_("zinc") = 26 xx 10^(-6) K^(-1)`)

Options

A. `100.054` cm , `100.054`cm
B. `100.078 "cm" , 100.078"cm"`
C. `100.078 cm , 100.054`cm
D. `100.054` cm , `100.078`cm

Answer

C

Explanation

At `30^(@)` true length is given by
=`SR (1+alpha_("zinc")DeltaT)`
=`100(1+26 xx 10^(-6) xx 30) = 100.078 `cm
At `0^(@)C`, True length is given by
=`(SR(1+alpha_("zinc")DeltaT))/((1+alpha_("glass")DeltaT)) = (100.078)/((1+8xx 10^(-6) xx 30))`
=`100.054`cm