$A$ 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 $2 \, mm$?

The unit of stress is:

$A$ lift is tied with thick iron ropes having mass $M$. The maximum acceleration of the lift is $a \ m/s^2$ and the maximum safe stress is $s \ N/m^2$. The minimum diameter of the rope is $(g = \text{acceleration due to gravity})$

$A$ composite heavy rope made of two materials is suspended vertically from a high ceiling. The ratios of different quantities for the upper rope to the lower rope are: length $\frac{L_u}{L_l} = \frac{1}{2}$,cross-sectional area $\frac{A_u}{A_l} = \frac{2}{1}$,and density $\frac{d_u}{d_l} = \frac{2}{3}$. What is the ratio of the maximum stress in the two ropes?

When a force $F_1$ is applied on a metallic wire, the length of the wire is $L_1$. If a force $F_2$ is applied on the same wire, the length of the wire is $L_2$. The original length of the wire $L$ is

The elastic limit of a metal is $\frac{400}{\pi} \text{ MPa}$. If a rod of this metal is to support a $484 \text{ N}$ load without exceeding its elastic limit, the minimum diameter of the rod is: (in $\text{ mm}$)