Answer:
0.0016 cm
Explanation:
[tex]\alpha_b[/tex] = Thermal coefficient of expansion of brass = [tex]19\times 10^{-6}\ /^{\circ}C[/tex]
[tex]\alpha_g[/tex] = Thermal coefficient of expansion of glass = [tex]9\times 10^{-6}\ /^{\circ}C[/tex]
[tex]\Delta T[/tex] = Change in temperature = [tex](60-20)^{\circ}C[/tex]
[tex]R_0[/tex] = Initial radius = 4 cm
Change in radius of material is given by
[tex]R=R_0(1+\alpha\Delta T)[/tex]
Difference in radii of the lid and jar
[tex]\Delta R=R_b-R_g\\\Rightarrow \Delta R=R_0(1+\alpha_b\Delta T)-R_0(1+\alpha_g\Delta T)\\\Rightarrow \Delta R=R_0(\alpha_b-\alpha_g)\Delta T\\\Rightarrow \Delta R=4\times (19\times 10^{-6}-9\times 10^{-6})\times (60-20)\\\Rightarrow \Delta R=0.0016\ cm[/tex]
The size of the gap is 0.0016 cm or 0.000016 m
