$A$ 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 $2 \, mm$?

$A$ 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?

$A$ $50 \;kg$ girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter $1.0 \;cm$. What is the pressure exerted by the heel on the horizontal floor?

Consider a long steel bar under a tensile stress due to force $F$ acting at the edges along the length of the bar (as shown in figure). Consider a plane making an angle $\theta$ with the length. What are the tensile and shearing stresses on this plane?
$(a)$ For what angle is the tensile stress a maximum?
$(b)$ For what angle is the shearing stress a maximum?

When a heavy weight is suspended from a metal wire and then removed,the wire does not regain its original length. Why?

Define plastic deformation and tensile strength.