A bimetallic strip made of materials X and Y, with linear expansion coefficients $\alpha_X$ and $\alpha_Y$ respectively ($\alpha_X > \alpha_Y$), is fixed at one end. When heated, the strip bends. A small mass 'm' is attached to the free end, producing a bending moment 'M'. If the temperature is further increased by $\Delta T$, and assuming the bending remains elastic, the additional bending moment required to keep the strip straight is:

The diameter of iron wheel is 1cm. If its temperature is increased by ${700^0}C$ what is the increase in circumference of the wheel? \left( {\alpha = 12 imes {{10}^{ - 6}}/{\,^0}C} \right)

The length of a metal rod at ${0^0}C$ is $0.5\,m$. When it is heated, its length increases by $2.7\,mm$. The final temperature of rod is $\left[ {\alpha = 90 imes {{10}^{ - 61}}^0C} \right]$

Two rods of materials X and Y have coefficients of linear expansion $\alpha_x$ and $\alpha_y$ and lengths $l_x$ and $l_y$ respectively. The difference in their lengths $(l_y - l_x)$ remains constant with temperature. What is the relationship between $\alpha_x$, $\alpha_y$, $l_x$, and $l_y$?

A bimetallic strip is constructed from two metals with lengths $l_1$ and $l_2$ and coefficients of linear expansion $\alpha_1$ and $\alpha_2$ respectively. If the difference in lengths $(l_2 - l_1)$ is designed to remain constant with changing temperature, what relationship must exist between $l_1$, $l_2$, $\alpha_1$, and $\alpha_2$?

Which of the following is the correct unit for the coefficient of linear expansion?

A pendulum clock keeps correct time at $20^\circ C$. The pendulum is made of a material with a linear expansion coefficient $\alpha$. If the temperature increases to $30^\circ C$, how much time will the clock gain or lose in one day?

Two thermometers $A$ and $B$ are exposed in sun light. The valve of is pointed black, but that of $B$ is not pointed. The correct statement regarding this case is

Two rods, one of invar and the other of steel, have lengths $l_i$ and $l_s$ respectively. Their coefficients of linear expansion are $\alpha_i$ and $\alpha_s$. If the difference in their lengths, $(l_s - l_i)$, remains constant as temperature changes, which of the following is true?

A wheel is 80.3 cm in circumference. An iron tyre measures 80.0 cm around its inner face. If the coefficient of linear expansion for iron is $12 imes {10^{ - 6}}^ \circ {C^{ - 1}}$, the temperature of the tyre must be raised by

Two rods of different materials but of the same length and cross-sectional area are heated through the same temperature difference. If their linear expansivities are $\alpha_1$ and $\alpha_2$ respectively, the difference in their elongation is: