$A$ $14.5\; kg$ mass,fastened to the end of a steel wire of unstretched length $1.0\; m$,is whirled in a vertical circle with an angular velocity of $2\; rev/s$ at the bottom of the circle. The cross-sectional area of the wire is $0.065\; cm^2$. Calculate the elongation of the wire when the mass is at the lowest point of its path.

$A$ 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?

When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end,its length increases by $l$. If the radius of the wire and the applied force were halved,then the increase in its length is

Two wires of the same length and material are stretched by the same force. If their masses are in the ratio $3:4$,then the ratio of their elongations is

Two metal wires $A$ and $B$ have lengths $L$ and $3L$ respectively. The radii of the cross-sectional circular areas of wires $A$ and $B$ are $R$ and $2R$, respectively. These wires are joined end-to-end along their axis. When one end of the combined system is fixed and the other end is pulled with a constant force $F$, the elongation in both wires is equal. If $Y_A$ and $Y_B$ are the Young's moduli of wires $A$ and $B$, respectively, then the ratio $Y_B / Y_A$ is:

The ratio of the lengths of two wires $A$ and $B$ of the same material is $1 : 2$ and the ratio of their diameters is $2 : 1$. If they are stretched by the same force,what is the ratio of the increase in their lengths?