A uniform solid sphere of radius 10 cm has a radius of gyration of 11 cm about an axis parallel to its diameter. The perpendicular distance of this axis from the centre of the sphere is ________ cm .

Step-by-step solution

Using the parallel axis theorem for the radius of gyration: k^2 = k_ cm ^2 + d^2 For a uniform solid sphere, the square of the radius of gyration about its central diameter is: k_ cm ^2 = 2 5 R^2 Given R = 10 cm and k = 11 cm : (11)^2 = 2 5 (10)^2 + d^2 121 = 40 + d^2 d^2 = 81 d = 9 cm Answer: 9