NEET2003PhysicsRotational MotionActual
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K . If radius of the ball be R , then the fraction of total energy associated with its rotational energy will be:
Options
- AK^2+R^2 R^2
- BK^2 R^2
- CK^2 K^2+R^2
- DR^2 K^2+R^2
Correct answer
C. K^2 K^2+R^2
Step-by-step solution
Total energy = 1 2 I ^2+ 1 2 m v^2= 1 2 m v^2 (1+ K^2 R^2 ) aligned & Rotational energy = 1 2 I ^2 & = K^2+R^2 1+ K^2 R^2 aligned aligned & Required fraction = K^2 / R^2 1+K^2 / R^2 & = K^2 R^2+K^2 aligned