For rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x 5 . The value of x is _____.

Step-by-step solution

The rotational kinetic energy is given by K r o t = I ω 2 2 = 1 3 M R 2 ω 2 . The total kinetic energy is given by K t o t = 1 2 m v 2 + 1 3 M R 2 ω 2 = m R 2 ω 2 2 + 1 3 M R 2 ω 2 = 5 6 M R 2 ω 2 Thus, the ratio is K r o t K t o t = 1 3 M R 2 ω 2 5 6 M R 2 ω 2 = 2 5 Comparing with the given value, x 5 = 2 5 ⇒ x = 2