A disc of mass `m` and radius `R` is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass `m//2` each are placed in it on either side of the centre of the disc as shown in Fig. The disc is given an initial angular velocity `omega_(0)` and released.

The angular speed of the disc when the balls reach the end of the disc is

Options

A. `(2mR^(2)omega_(0)^(2))/9`
B. `(mR^(2)omega_(0)^(2))/18`
C. `(mR^(2)omega_(0)^(2))/6`
D. `(mR^(2)omega_(0)^(2))/9`

Answer

D

Explanation

Work done by all force is equal
`K_(f)-K_(i)=1/2(m/2)v^(2)=(mR^(2)omega_(0)^(2))/9`