$A$ force of $1000 \, N$ is required to break a copper wire of radius $1 \, mm$. What force is required to break a copper wire of radius $2 \, mm$?

Why is rubber used to make cycle seats instead of wood or iron?

$A$ rod of constant cross-section moves towards the right with constant acceleration $a$. The graph of stress versus distance from the left end is shown in the figure. If the density of the material of the rod at cross-section $1$ is $9 \text{ g/cm}^3$,find the density at cross-section $2$ in $\text{g/cm}^3$.

Two wires as shown in the figure below, made of steel, have a breaking stress of $12 \times 10^8 \text{ N/m}^2$. The area of cross-section of the upper wire is $0.008 \text{ cm}^2$ and that of the lower wire is $0.004 \text{ cm}^2$. The maximum mass that can be added to the pan without breaking any wire is . . . . . . kg. (Take $g = 10 \text{ m/s}^2$)

The lower surface of a cube is fixed. On its upper surface,a force is applied at an angle of $30^{\circ}$ from its surface. The change will be of the type:

The increase in length is $l$ of a wire of length $L$ by the longitudinal stress. Then the stress is proportional to