$A$ pendulum clock keeps correct time at $0\,^{\circ}C$. The thermal coefficient of linear expansion of the material of the pendulum is $\alpha$. If the temperature rises to $t\,^{\circ}C$,then the clock loses per day by (in seconds):

The volume of a metal sphere increases by $0.30 \%$,when its temperature is raised by $50^{\circ} C$. The coefficient of linear expansion of the metal is

The difference in length between two rods $A$ and $B$ is $60 \ cm$ at all temperatures. If $\alpha_A = 18 \times 10^{-6} /^{\circ}C$ and $\alpha_B = 27 \times 10^{-6} /^{\circ}C$,then the lengths of rod $A$ and rod $B$ at $0^{\circ}C$ are respectively:

If a cylinder is heated such that its length increases by $2\%$,then its base area will increase by ......... $(\%)$.

An aluminium and steel rod having same lengths and cross-sections are joined to make a total length of $120 \ cm$ at $30^{\circ} C$. The coefficients of linear expansion of aluminium and steel are $24 \times 10^{-6} /{ }^{\circ} C$ and $1.2 \times 10^{-5} /{ }^{\circ} C$, respectively. The length of this composite rod when its temperature is raised to $100^{\circ} C$, is . . . . . . $cm$. (in $cm$)

The coefficient of superficial expansion of a solid is $2 \times 10^{-5} \text{ °C}^{-1}$. Its coefficient of linear expansion is: