If the volume of a block of metal changes by $0.12\%$ when it is heated through $20\,^{\circ}C$,the coefficient of linear expansion (in $^{\circ}C^{-1}$) of the metal is

Two rods,one of aluminium and the other of steel,having initial lengths $L_1$ and $L_2$ are connected together to form a single rod of length $(L_1+L_2)$. The coefficients of linear expansion of aluminium and steel are $\alpha_1$ and $\alpha_2$ respectively. If the length of each rod increases by the same amount,when their temperatures are raised by $t^{\circ}C$,then the ratio $\frac{L_1}{L_1+L_2}$ will be

When a copper sphere is heated,in which of the following will the maximum percentage change be observed?

$A$ brass disc fits snugly in a hole of a steel plate. The disc can be loosened from the hole if the system:

The ratio among the linear expansion coefficient $(\alpha)$,areal expansion coefficient $(\beta)$,and volume expansion coefficient $(\gamma)$ is:

The focal length of a spherical mirror made of steel is $150 \,cm$. If the temperature of the mirror increases by $200 \,K$, its focal length becomes (coefficient of linear expansion of steel $\alpha = 12 \times 10^{-6} \,^{\circ}C^{-1}$). (in $\,cm$)