In figure (a) there is a uniform cylinder of mass M and radius R. Length of the cylinder is `L = sqrt3R`. The cylinder is rolling without sliding on a horizontal surface with its centre moving at speed V. In figure (b) the same cylinder is moving on a horizontal surface with its centre moving at speed V and the cylinder rotating about a vertical axis passing through its centre. [Place your pencil on the table and give a sharp blow at its end. Look at the motion of the pencil. This is how the cylinder is moving]. The angular speed is `omega = (V)/(R)`. Write the kinetic energy of the cylinder in two cases. In which case, the kinetic energy would have been higher if length of the cylinder were doubled `(= 2 sqrt3 R)`.
(a)

Answer

`(3)/(4) MV^(2)` in both case. In case (b) the Kinetic energy will be higher if length was doubled.