A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. A shear force of 10⁵ N is applied at the top. If the shear modulus is 10¹⁰ N/m² and deformation is very small, the angular displacement θ of the rod axis is:
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Question

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. A shear force of 10⁵ N is applied at the top. If the shear modulus is 10¹⁰ N/m² and deformation is very small, the angular displacement θ of the rod axis is:

Options

G1 Physics · Accepted Answer

For small shear deformation, shear strain ≈ θ. Shear stress is F/A, where A = πr². Shear modulus: η = (F/A)/θ. Therefore, θ = F/(Aη) = F/(πr²η). Given, F = 10⁵ N, r = 4 cm = 0.04 m, η = 10¹⁰ N/m². Thus, θ = 10⁵/[π(0.04)²(10¹⁰)] = 10⁵/[π(1.6×10⁻³)(10¹⁰)] = 1/(160π). Correct option: B.