A disc of mass 'm' and radius R is free to rotate in horizontal plane about a vetical smooth fixed axis passing through is 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 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. `(omega_(0))/(2)`
B. `(omega_(0))/(3)`
C. `(2omega_(0))/(3)`
D. `(omega_(0))/(4)`

Answer

2

Explanation

Let the angular speed of disc when the balls reach the end be `omega`. From conservation of angular momentum
`(1)/(2)mR^(2)omega_(0)=(1)/(2)mR^(2)omega+("m")/(2)R^(2)omega+("m")/(2)R^(2)omega`
`omega=(omega_(0))/(3)`