A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively k s p h : k c y l is 2 : x . The value of x is _______.

Step-by-step solution

Considering rotational axis as the diametrical axis for sphere and axis of cylinder. Then K 1 2 = 2 5 R 2 and K 2 2 = 1 2 R 2 ∴   K 1 K 2 = 2 / 5 1 / 2 = 4 5 ⇒ K 1 K 2 = 2 5 Comparing it with the given value in the question, 2 5 = 2 x ∴ x = 5