A uniform disc of radius a and mass m, is rotating freely with angular speed `omega` in a horizontal plane. About a smooth fixed vertical axis through its centre. A particle, also of mass m, is suddently attached to the rim of the disc of the disc and rotates with it. The new angular speed is

Options

A. `(omega)/(6)`
B. `(omega)/(3)`
C. `(omega)/(2)`
D. `(omega)/(5)`

Answer

B

Explanation

From the conservation of angular momentum, `I_(1)omega_(1)=I_(2)omega_(2)`
`:. omega_(2)=(I_(1))/(I_(2)).omega_(1)=((1//2ma^(2)))/((1//2ma^(2))+ma^(2)).omega=(omega)/(3)`.