An aluminium sphere of $20 \; cm$ diameter is heated from $0^{\circ} C$ to $100^{\circ} C$. Its volume changes by (given that coefficient of linear expansion for aluminium $\alpha_{Al} = 23 \times 10^{-6} \; /^{\circ} C$): (in $; cm^3$)

Three rods of length $\ell$ each are joined to form an equilateral triangle $PQR$. $O$ is the midpoint of $PQ$. For a small change in temperature,the distance $OR$ remains constant. If the coefficient of linear expansion for $PR$ and $RQ$ is $\alpha_2$ and for $PQ$ is $\alpha_1$,then:

When a bimetallic strip is heated, it

Two rods,one of copper $(Cu)$ and the other of iron $(Fe)$,having initial lengths $L_1$ and $L_2$ respectively,are connected together to form a single rod of length $L_1+L_2$. The coefficients of linear expansion of $Cu$ and $Fe$ are $\alpha_c$ and $\alpha_i$ respectively. If the length of each rod increases by the same amount when their temperatures are raised by $t^{\circ}C$,then the ratio $\frac{L_1-L_2}{L_1+L_2}$ will be:

If the length of a cylinder on heating increases by $2\%$,the area of its base will increase by ....... $\%$

$A$ metal rod $2 \,m$ long increases in length by $1.6 \,mm$, when heated from $0^{\circ} C$ to $60^{\circ} C$. The coefficient of linear expansion of the metal rod is: