$A$ cable is cut to half of its original length. What will be the effect on the increase in its length under a given load?

Write the equation of bending in a rod. Write the unit of bending and its dimensional formula.

$A$ copper wire and an aluminium wire have lengths in the ratio $5: 2$, diameters in the ratio $4: 3$ and forces applied in the ratio $4: 5$. Find the ratio of increase in length of the copper wire to that of the aluminium wire. (Given: $Y_{Cu} = 1.1 \times 10^{11} \text{ Nm}^{-2}$, $Y_{Al} = 0.7 \times 10^{11} \text{ Nm}^{-2}$)

The length of an elastic string is $x \, m$ when the tension is $8 \, N$ and $y \, m$ when the tension is $10 \, N$. The length in meters when the tension is $18 \, N$ is:

If the temperature of a wire of length $2 \,m$ and area of cross-section $1 \,cm^2$ is increased from $0^{\circ}C$ to $80^{\circ}C$ and is not allowed to increase in length,then the force required for it is ............$N$ $\{Y=10^{10} \,N/m^2, \alpha=10^{-6}/^{\circ}C\}$

$A$ 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?