A cube of side 5 cm has modulus of rigidity 10⁵ N·m⁻². A tangential force of 10 N is applied to the upper face while the lower face is fixed. If the resulting lateral displacement of the upper face is N mm, find N.

Question

G1 Physics · Accepted Answer

Modulus of rigidity is η = shear stress ÷ shear strain. For the cube, shear stress = F ÷ A and shear strain = x ÷ h. Therefore, η = (F ÷ A) ÷ (x ÷ h) = Fh ÷ (Ax). Hence, x = Fh ÷ (Aη). Given, F = 10 N, h = 5 cm = 5×10⁻² m, A = (5×10⁻²)² = 25×10⁻⁴ m², η = 10⁵ N·m⁻². Thus, x = 10×5×10⁻² ÷ [(25×10⁻⁴)(10⁵)] = 2×10⁻³ m = 2 mm. Therefore N = 2.