Define shearing stress and write its formula.

$A$ rod of length $2 \ m$ rests on a smooth horizontal floor. If the rod is heated from $0^\circ C$ to $20^\circ C$,find the longitudinal strain developed? $(\alpha = 5 \times 10^{-5} / ^\circ C)$

$A$ lift of mass $1600 \text{ kg}$ is supported by a thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^8 \text{ N/m}^2$ and its radius is $4 \text{ mm}$, then the maximum acceleration the lift can take is . . . . . . $\text{m/s}^2$. (Take $g = 10 \text{ m/s}^2$ and $\pi = 3.14$)

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:

Anvils made of single crystals of diamond,with the shape as shown in the figure,are used to investigate the behavior of materials under very high pressures. The flat faces at the narrow end of the anvil have a diameter of $0.50 \; mm$,and the wide ends are subjected to a compressional force of $50,000 \; N$. What is the pressure at the tip of the anvil?

$A$ 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?