A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is a 3 R 2 ω . The value of a will be

Step-by-step solution

Angular momentum of a rotating and translating body is given by, L O = m v R + I ω = m v R + 2 3 M R 2 ω For rolling, v = ω R ⇒ L O = m ω R 2 1 + 2 3 = 5 3 m ω R 2 Therefore, the value of a = 5 .