Two similar beads each of mass m slide smoothly along a uniform rod of mass M and length l. The rod can rotate along an axis passing through its centre and normal to its length. Initially the rod is rotated with angular speed `omega_1` when beads are at the centre C of the rod. The angular speed of of the rod when beads slide to the two ends of the rod without any external force is given by

Options

A. `((M + m)omega_i)/(Mm)`
B. `(Momega_i)/((6m + M))`
C. `(Mm)/(M + m) omega_i`
D. `(2 m omega_i)/((M + 2m))`1/2

Answer

B

Explanation

Using `I omega `= constant : `I_i omega_i = I_f omega_f , I_i = (Ml^2)/12`
Here `I_f = (Ml^2)/12 + 2m (l/2)^2 = (Ml^2)/12 + (ml^2)/2 " " therefore omega_f = (Momega_i)/((6 m + M))`