A uniform disk of mass `300kg` is rotating freely about a vertical axis through its centre with constant angular velocity `omega .` A boy of mass `30kg` starts from the centre and moves along a radius to the edge of the disk. The angular velocity of the disk now is

Options

A. `(w_(0))/(6 )`
B. `(w_(0))/(5 )`
C. ` (4 omega_(0))/(5)`
D. `(5 omega_(0))/(6)`

Answer

D

Explanation

As `sumtau = 0` angular momentum remains conseved:
`:. L = (0 + (300 R^(2))/(2 ) ) omega_(0)`
`= ((300 R^(2))/(2 ) + 30 R^(2)) omega `
`implies 150 omega_(0) = 180 omega implies omega = (5)/(6) omega_(0)`