Q4. A solid steel ball of volume 100 cm is placed in a fluid, and the pressure on it is raised by 1.0 × 10 Pa. Its volume decreases by 0.00625 cm. Find the increase in hydraulic stress and the volume strain.
The hydraulic stress rises by the same amount as the pressure, 1.0 × 10 Pa. The signed volume strain is −0.00625/100 = −6.25 × 10; the positive fractional compression is 6.25 × 10.
Q5. Two wires of the same material carry the same load. One has twice the diameter of the other. Compare the stresses in them.
Area goes as the square of the diameter, so the thicker wire has 4 times the area and one quarter of the stress. The stresses are in the ratio 1 : 4 (thick : thin).
Q6. A shearing force moves the top of a 5.0 cm thick rubber pad 1.0 mm sideways relative to its base. Find the shearing strain and the angle of shear in degrees.
Strain = 1.0 × 10/(5.0 × 10) = 0.02, so θ ≈ 0.02 rad, about 1.1°.