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 $\,cm$)

An iron rod of length $10 \ m$ is heated from $0 \ ^{\circ}C$ to $100 \ ^{\circ}C$. If the coefficient of linear expansion of iron is $10 \times 10^{-6} \ ^{\circ}C^{-1}$,then the increase in the length of the rod is ..... $cm$.

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40^{\circ}C$. The coefficient of linear expansion of the metal is .......... $^{\circ}C^{-1}$.

Three rods of equal lengths are joined to form an equilateral triangle $ABC$. $D$ is the mid-point of $AB$. The coefficient of linear expansion is $\alpha_1$ for the material of rod $AB$ and $\alpha_2$ for the material of rods $AC$ and $BC$. If the distance $DC$ remains constant for small changes in temperature, then:

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

An iron sphere having diameter $D$ and mass $M$ is immersed in hot water so that the temperature of the sphere increases by $\delta T$. If $\alpha$ is the coefficient of linear expansion of the iron,then the change in the surface area of the sphere is: