NTA Abhyas JEE Main2020PhysicsMechanical Properties of SolidsPractice
A cube of aluminium of side 6   cm is subjected to a tangential force such that the top face is shears through 0.012   cm relative to the bottom face. The tangential force is k × 10 10   dyne . What is the value of k ? [Shear modulus of the material is η = 2 × 10 11   dyne   cm - 2 ]
Correct answer
1.44
Step-by-step solution
Lateral displacement, x = 0 . 012 c m ∴ Shearing strain, θ = x L = 0 . 012 6 = 0 . 002 Shearing stress, F a = η θ = 2 × 10 11 × 0 . 002 = 4 × 10 8 dynecm - 2 Shearing force, F = shearing stress × area = 4 × 10 8 × ( L ) 2 = 4 × 10 8 × ( 6 ) 2 = 1 . 44 × 10 10 d y n e ⇒ K = 1 . 44