$A$ copper rod of $88\; cm$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminum rod is....$cm$.
$(\alpha_{Cu} = 1.7 \times 10^{-5}\; K^{-1}$ and $\alpha_{Al} = 2.2 \times 10^{-5}\; K^{-1})$

When the temperature of a body increases from $T$ to $T+\Delta T$, its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body, then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

The focal length of a spherical mirror made of steel is $150 \,cm$. If the temperature of the mirror increases by $200 \,K$, its focal length becomes (coefficient of linear expansion of steel $\alpha = 12 \times 10^{-6} \,^{\circ}C^{-1}$). (in $\,cm$)

Three uniform thin aluminium rods each of length $2 \,m$ form an equilateral triangle $PQR$ as shown in the figure. The midpoint of the rod $PQ$ is at the origin of the coordinate system. If the temperature of the system of rods increases by $50^{\circ} C$, the increase in $y$-coordinate of the centre of mass of the system of the rods is ............ $mm$. (Coefficient of volume expansion of aluminium $= 12 \sqrt{3} \times 10^{-6} \,K^{-1}$)

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 $100^{\circ} C$? $[\alpha_{\text{copper}} = 18 \times 10^{-6} /^{\circ} C]$

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \,m$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $= 10 \times 10^{-6} \,K^{-1}$) (in $^{\circ} C$)