$A$ seconds pendulum clock has a steel wire. The clock shows correct time at $25^{\circ} C$. How many seconds does the clock lose or gain in one week,when the temperature is increased to $35^{\circ} C$? (Given: $\alpha_{\text{steel}} = 1.2 \times 10^{-5} /^{\circ} C$)

The coefficients of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$ respectively. The lengths of the brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained the same at all temperatures,which one of the following relations is correct?

$A$ brass rod of length $50\; cm$ and diameter $3.0\; mm$ is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at $250\; ^{\circ}C$,if the original lengths are at $40.0\; ^{\circ}C$? Is there a 'thermal stress' developed at the junction? The ends of the rod are free to expand. (Coefficient of linear expansion of brass $= 2.0 \times 10^{-5}\; K^{-1}$,steel $= 1.2 \times 10^{-5}\; K^{-1}$)

The coefficient of linear expansion depends on

Two metal rods $A$ and $B$ each of length $50 \ cm$ and diameter $4.0 \ mm$ are joined together at temperature $30^{\circ} C$. What is the change in length of the combined rod at $230^{\circ} C$ (in $mm$)? [Given linear expansion coefficients of rods $A$ and $B$ are respectively,$2.0 \times 10^{-5} /^{\circ} C$ and $1.0 \times 10^{-5} /^{\circ} C$]

$A$ uniform metal rod is used as a bar pendulum. If the room temperature rises by $10^{\circ}C$,and the coefficient of linear expansion of the metal of the rod is $2 \times 10^{-6} /^{\circ}C$,the period of the pendulum will have a percentage increase of: