A cube has side length 5 cm and modulus of rigidity 10⁵ N/m². The displacement produced by a force of 10 N applied on the upper face is:

η = Shear Stress / Shear Strain

Shear stress:

= F/A

Shear strain:

= x/l

where:

• F = Applied force
• A = Area of face
• x = Displacement produced
• l = Length of cube

Therefore:

η = (F/A)/(x/l)

x = Fl/(ηA)

Given:

• F = 10 N
• l = 5 cm = 0.05 m
• A = (0.05)² = 0.0025 m²
• η = 10⁵ N/m²

Substituting:

x = (10 × 0.05)/(10⁵ × 0.0025)

x = 0.002 m

Converting to centimeters:

x = 0.2 cm

The modulus of rigidity measures the resistance of a material to shape deformation. Materials with a larger shear modulus undergo smaller deformation for the same applied force.

Hence, the displacement produced is:

0.2 cm