A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is n ~cm . The value of n is

Step-by-step solution

Using the parallel axis theorem for radius of gyration: k^2 = k_ cm ^2 + d^2 where k_ cm is the radius of gyration about the center of mass and d is the distance from the center. For a solid sphere: I_ center = 2 5 MR^2 , so k_ cm ^2 = 2 5 R^2 With R = 10 cm and d = 15 cm: k^2 = 2 5 (10)^2 + (15)^2 = 40 + 225 = 265 Since k = n , we have n = 265 .