$A$ 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 side of a copper cube is $1 \ m$ at $0^{\circ} C$. What will be the change in its volume,when it is heated to $100^{\circ} C$? $[\alpha_{\text{copper}} = 18 \times 10^{-6} /^{\circ} C]$

Two rods,one of aluminum and the other made of steel,having initial lengths $l_1$ and $l_2$ are connected together to form a single rod of length $l_1 + l_2$. The coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively. If the length of each rod increases by the same amount when their temperature is raised by $t ^\circ C$,then find the ratio $\frac{l_1}{l_1 + l_2}$.

At what temperature (in $ ^{\circ} C$) should a gold ring of diameter $6.230 \,cm$ be heated so that it can be fitted on a wooden bangle of diameter $6.241 \,cm$ (in $.7$)? Both diameters were measured at room temperature $(27^{\circ} C)$. (Given: coefficient of linear thermal expansion of gold $\alpha_{L}=1.4 \times 10^{-5} \,K ^{-1}$)

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

Show that the coefficient of area expansion,$(\Delta A / A) / \Delta T,$ of a rectangular sheet of a solid is twice its linear expansivity,$\alpha_{l}$.