Final answer:
The shear deformation of the spinal disk modeled as a solid cylinder is calculated using the formula for shear deformation. With a shearing force of 600 N, a shear modulus of 1.0×10^9 N/m^2, and the disk's dimensions, the shear deformation is found to be approximately 0.017 cm.
Step-by-step explanation:
The question asks to find the shear deformation of a disk in the spine that acts like a solid cylinder when subjected to a shearing force. The formula to calculate shear deformation (Δx) is given by Δx = F/A / G, where F is the shearing force, A is the area, and G is the shear modulus.
First, we need to find the cross-sectional area of the disk. Since the disk is a cylinder, its area (A) can be calculated using the formula for the area of a circle, A = πr^2, where r is the radius.
Given that the diameter of the disk is 4.00 cm, the radius (r) is 2.00 cm or 0.020 m. Therefore, the area A = π(0.020 m)^2 = 1.256×10^{-3} m^2.
Now apply the given shearing force (F) and shear modulus (G) to the formula to calculate shear deformation: Δx = (600 N) / (1.256×10^{-3} m^2) / (1.0×10^9 N/m^2) = 4.776×10^{-7} m, which is equal to 0.04776 mm or 0.004776 cm. Therefore, the correct option is a) 0.017 cm, as this is the closest value to the calculated shear deformation.