When a body is heated, then the maximum rise will be in its

Obtain the relation between the coefficient of volume expansion $(\alpha_V)$ and the coefficient of linear expansion $(\alpha_l)$.

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 $cm$)

$A$ circular disc with a hole is shown in the figure. On heating,if the outer diameter $d_1$ increases by $0.3\%$,then the inner diameter $d_2$ will

The coefficient of volume expansion of a material is $5 \times 10^{-4} {^{\circ}C}^{-1}$. The fractional change in its density for a $40^{\circ}C$ rise in temperature is nearly.

$A$ copper rod of length $l_1$ and an iron rod of length $l_2$ are always maintained at the same common temperature $T$. If the difference $(l_2 - l_1)$ is $15\,cm$ and is independent of the value of $T$,then $l_1$ and $l_2$ have the values (given the linear coefficients of expansion for copper and iron are $\alpha_c = 2.0 \times 10^{-6}\,^{\circ}C^{-1}$ and $\alpha_i = 1.0 \times 10^{-6}\,^{\circ}C^{-1}$ respectively).