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 ]

Question

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 ],

MARKS App · Accepted Answer

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

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