$A$ metallic rod having area of cross-section $A$,Young's modulus $Y$,coefficient of linear expansion $\alpha$,and length $L$ is tied between two strong pillars. If the rod is heated through a temperature $t \, ^\circ C$,then how much force is produced in the rod?

Which one of the following substances possesses the highest elasticity?

$A$ metal string $A$ is suspended from a rigid support and its free end is attached to a block of mass $M$. $A$ second block having mass $2M$ is suspended at the bottom of the first block using a string $B$. The area of cross-sections of strings $A$ and $B$ are the same. The ratio of lengths of strings $A$ to $B$ is $2$ and the ratio of their Young's moduli $(Y_A/Y_B)$ is $0.5$. The ratio of elongations in $A$ to $B$ is . . . . . . .

Young's moduli of the material of wires $A$ and $B$ are in the ratio of $1: 4$,while their areas of cross-section are in the ratio of $1: 3$. If the same amount of load is applied to both the wires,the amount of elongation produced in the wires $A$ and $B$ will be in the ratio of [Assume length of wires $A$ and $B$ are same].

$A$ wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel,it is heated so that its temperature rises by $\Delta T$ and it just slips over the wheel. As it cools down to the surrounding temperature,it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$,and its Young's modulus is $Y$,the force that one part of the wheel applies on the other part is:

$A$ wire of length $0.5 \ m$ and area of cross-section $4 \times 10^{-6} \ m^2$ at a temperature of $100^{\circ} C$ is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to $0^{\circ} C$,but is prevented from contracting,by attaching a mass at the lower end. If the mass of the wire is negligible,then the value of the mass attached to the wire is (Young's modulus of material of the wire $= 10^{11} \ N \ m^{-2}$; coefficient of linear expansion of the material of the wire $= 10^{-5} \ K^{-1}$ and acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $kg$)