The coefficient of linear expansion of a crystalline substance in one direction is $2 \times 10^{-4} /{ }^{\circ} C$ and in every direction perpendicular to it is $3 \times 10^{-4} /{ }^{\circ} C$. The coefficient of cubical expansion of the crystal is equal to ........... $\times 10^{-4} /{ }^{\circ} C$.

$A$ metal rod of silver at $0^{\circ}C$ is heated to $100^{\circ}C$. Its length increases by $0.19\, cm$. If the original length of the rod is $100\, cm$,the coefficient of cubical expansion of the silver rod is:

Three rods of equal length $l$ are joined to form an equilateral triangle $PQR.$ $O$ is the midpoint of $PQ.$ The distance $OR$ remains the same for a small change in temperature. The coefficient of linear expansion for $PR$ and $RQ$ is the same,i.e.,$\alpha_2,$ but that for $PQ$ is $\alpha_1.$ Then:

The volume of a metal sphere increases by $0.33 \%$ when its temperature is raised by $50^{\circ} C$. The coefficient of linear expansion of the metal is

$A$ pendulum clock loses $12\;s$ a day if the temperature is $40^{\circ}C$ and gains $4\;s$ a day if the temperature is $20^{\circ}C$. The temperature at which the clock will show correct time,and the coefficient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively:

$A$ uniform metal rod of length $L$ and mass $M$ is rotating about an axis passing through one of the ends and perpendicular to the rod with angular speed $\omega$. If the temperature increases by $t^{\circ} C$, then the change in its angular velocity is proportional to which of the following? (Coefficient of linear expansion of rod $= \alpha$)