A circular metallic ring of radius $R$ has a small gap of width $d$. The coefficient of thermal expansion of the metal is $\alpha$ in appropriate units. If we increase the temperature of the ring by an amount $\Delta T$, then width of the gap
will increase by an amount $d \alpha \Delta T$
will not change
will increase by an amount $(2 \pi R-d) \alpha \Delta T$
will decrease by an amount $d \alpha \Delta T$
A rail track made of steel having length $10\,m$ is clamped on a railway line at its two ends as shown in figure. On a summer day due to rise in temperature by $20\,^oC$ , it is deformed as shown in figure. Find $x$ (displacement of the centre) if $\alpha _{steel} = 1.2 \times 10^{-5} \,^oC^{-1}$
Show that the coefficient of area expansion, $(\Delta A / A) / \Delta T,$ of a rectangular sheet of the solid is twice its Iinear expansivity, $\alpha_{1}$
The coefficient of apparent expansion of mercury in a glass vessel is $132 ×\times10^{-6}/^oC$ and in a steel vessel is $114 \times 10^{-6}/^oC$ . If $\alpha $ for steel is $12 \times 10^{-6}/^oC$ , then that of glass is
If two rods of length $L$ and $2L$ having coefficients of linear expansion $\alpha$ and $2\alpha$ respectively are connected so that total length becomes $3L$, the average coefficient of linear expansion of the composition rod equals:
The density of water at $20^oC$ is $0.998\ gm/cm^3$ and at $40^oC$ is $0.992\ gm/cm^3$. The mean coefficient of cubical expansion (in per ${}^oC$) is