A solid metal cylinder is fixed at its bottom end. A tangential force of 360 N is applied to its top face, producing an angular displacement of 10⁻⁵ rad in the cylinder. If the shear modulus of the material is 10¹⁰ N/m ^2 , the diameter of the cylinder is :

Step-by-step solution

Given tangential force F = 360 N , angular displacement = 10⁻⁵ rad , and shear modulus G = 10¹⁰ N/m ^2 . The shear modulus is given by G = F A , where A is the cross-sectional area. Rearranging for A : A = F G = 360 10¹⁰ 10⁻⁵ = 36 10⁻⁴ m ^2 Since A = r^2 , we have: r^2 = 36 10⁻⁴ r = 6 10⁻² m = 6 cm The diameter of the cylinder is D = 2r = 12 cm . Answer: 12 cm