Question

For solids with elastic modulus of rigidity, the shearing force is proportional to _____ while for fluids it is proportional to _____ (shear strain / rate of shear strain). Fill in the blank.

Answer 1

shear strain , rate of shear strain.

for solid , shear modulus = shear stress/shear strain
or, shear modulus = shear force/area × shear strain
or, shear force = (shear modulus × area) × shear strain
here it is clear that shearing force is directly proportional to shear strain .

for fluid , shearing force is directly proportional to rate of shear strain.
actually, the fluid has tendency to flow and reach some velocity before it reaches a steady state with some velocity gradient.
Now having a velocity gradient means that with time each point in the fluid will change it's position with time therefore the strain is not constant and there is a strain rate. and this strain rate is proportional to the applied shear force/stress .

that's why shearing force is directly proportional to rate of strain.