A uniform rod of mass m and length L lies radialy on a disc rotating with angular speed `omega` in a horizontal plane about vertical axis passing thorugh centre of disc. The rod does not slip on the disc and the centre of the rod is at a distance 2L from the centre of the disc. them the kinetic energy of the rod is

Options

A. `1/2m omega^(2)(R^(2) + L^(2)/12)`
B. `1/2 M omega^(2)R^(2)`
C. `1/24 M omega^(2) L^(2)`
D. None of these

Answer

A

Explanation

Moment of inertia of the rod w.r.t. the axis through the centre of the disc is (by parallel axis theorem),
`I =(mL^(2))/12 + mR^(2)` K.E. of the rod `=1/2 Iomega^(2) = 1/2 m omega^(2) [R^(2) + L^(2)/12]`